On a common refinement of Stark units and Gross–Stark units: On a common refinement of Stark units and Gross-Stark units

Συγγραφείς: Kashio, Tomokazu

Πηγή: Journal of the London Mathematical Society. 111

Θεματικοί όροι: Mathematics - Number Theory, Analytic theory of abelian varieties, abelian integrals and differentials, Zeta functions and \(L\)-functions, 11G15, 11R27, 11R37, 11R42, 11R80, 11S40, 11S80, 14F30, 14K20, 14K22, 33B15, Complex multiplication and moduli of abelian varieties, Units and factorization, Class field theory, \(p\)-adic cohomology, crystalline cohomology, 01 natural sciences, Totally real fields, FOS: Mathematics, Zeta functions and \(L\)-functions of number fields, Complex multiplication and abelian varieties, Number Theory (math.NT), 0101 mathematics, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Gamma, beta and polygamma functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1706.03198

Upper Bounds for Shifted Moments of Quadratic Dirichlet L-Functions over Function Fields: Upper bounds for shifted moments of quadratic Dirichlet \(L\)-functions over function fields

Συγγραφείς: Peng Gao, Liangyi Zhao

Πηγή: Hardy-Ramanujan Journal.

Θεματικοί όροι: upper bounds, Mathematics - Number Theory, quadratic Dirichlet \(L\)-functions, shifted moments, FOS: Mathematics, Zeta functions and \(L\)-functions of function fields, quadratic Dirichlet character sums, Number Theory (math.NT), Zeta and \(L\)-functions in characteristic \(p\), 11M38, 11R59, 11T06, Polynomials over finite fields

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2408.02880

Geometric main conjectures in function fields

Συγγραφείς: Bley, Werner, Popescu, Cristian D.

Πηγή: Journal für die reine und angewandte Mathematik (Crelles Journal).

Θεματικοί όροι: Arithmetic theory of algebraic function fields, Mathematics - Number Theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), FOS: Mathematics, Integral representations related to algebraic numbers, Galois module structure of rings of integers, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT), Zeta and \(L\)-functions in characteristic \(p\), 0101 mathematics, 11G09, 11G20, 11R59, 11M38, 11R23, 11R37, 11R34, 01 natural sciences, Iwasawa theory

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2209.02440

Validator-Grade Synthesis of the Langlands Correspondence via Spectral Functoriality, Arithmetic Regulators, Geometric Duality, and Universal Trace Propagation

Συγγραφείς: Forrest M. Anderson, Forrest

Θεματικοί όροι: Langlands Program Langlands Correspondence Grand Langlands Conjecture Automorphic Forms Automorphic Representations Galois Representations Modular Forms L-functions Motives Number Theory Representation Theory Arithmetic Geometry Algebraic Geometry Moduli Spaces Shimura Varieties Tannakian Categories Hecke Algebras Parabolic Subgroups Satake Isomorphism Trace Formula Arthur's Trace Formula Endoscopy Theory Functoriality Principle Harmonic Analysis on Reductive Groups Reductive Algebraic Groups Automorphic L-functions Cuspidal Representations Adelic Groups Theta Correspondence Unramified Representations Tempered Representations Galois Deformations P-adic Hodge Theory Geometric Langlands Program Topos Theory Derived Algebraic Geometry Perverse Sheaves D-modules Categorical Langlands Correspondence Affine Grassmannian Loop Groups Geometric Satake Equivalence Shtukas Étale Cohomology Torsors Modular Curves Langlands Dual Group Langlands Reciprocity Frobenius Morphism Local-Global Principle Arithmetic Duality Zeta Functions Motivic L-functions Lafforgue Correspondence V. Lafforgue Robert Langlands Ngo Bao Chau Wiles–Taylor Modular Lifting Fermat's Last Theorem Drinfeld Modules Shimura-Taniyama Conjecture Sato–Tate Conjecture Serre's Modularity Conjecture, Langlands Program, Grand Langlands Conjecture, Spectral Functoriality, Arithmetic Regulator, Geometric Langlands, Automorphic Representations, Motives, Motivic Cohomology, Derived Algebraic Geometry, D-modules, Perverse Sheaves, Hecke Operators, Affine Grassmannian, Moduli Stacks, Local Systems, Langlands Dual Group, Functional Equations, L-functions, Trace Formula, Frobenius Trace, Interval Arithmetic, LU Decomposition, Determinant Identity, Regulator Maps, Categorical Equivalence, Kernel Transforms, Fourier-Mukai Functor, Derived Categories, Tannakian Formalism, Spectral Stacks, Arithmetic Geometry, Algebraic Groups, Representation Theory, Algebraic Topology, Homotopical Algebra, Derived Stacks, Categorical Descent, Spectral Gluing, Validator-Grade Proofs, Replication Frameworks, Mathematical Physics, Number Theory, Algebraic Geometry, Non-Abelian Hodge Theory, Geometric Satake Equivalence, Beilinson-Drinfeld, Deligne, Grothendieck, Voevodsky, Frenkel, Gaitsgory, Lurie, Mirkovié-Vilonen, Jacquet-Langlands, Arthur Trace Formula, Ngo Fundamental Lemma, Local Langlands Correspondence, Global Langlands Correspondence, p-adic Langlands Program, Langlands Parameters, L-packets, Endoscopy Theory, Stabilization of the Trace Formula, Base Change, Liftings, Langlands–Shahidi Method, Converse Theorems, Langlands–Deligne Conjecture, Langlands–Rapoport Conjecture, Langlands–Tunnell Theorem, Ran Space, Factorization Algebras, Chiral Algebras, Twisted Sheaves, Ind-schemes, Loop Groups, Perfectoid Spaces, Diamonds, Prismatic Cohomology, Crystalline Cohomology, Rigid-Analytic Spaces, Infinity Categories, ∞-categories, Higher Topos Theory, Sheaf Theory in ∞-categories, Spectral Algebraic Geometry, Stable ∞-categories, Simplicial Presheaves, Model Categories, Homotopy Type Theory, Motivic Homotopy Theory, A¹-homotopy, Mirror Symmetry, S-duality, Topological Quantum Field Theory, Extended TQFTs, Kapustin–Witten Correspondence, Betti Moduli, de Rham Moduli, Dolbeault Moduli, Hodge Filtration, Hitchin Fibration, Nonabelian Poincaré Duality, Modularity Lifting Theorems, Galois Deformation Rings, Shimura Varieties, Eigenvarieties, Cohomology of Arithmetic Groups, Mod p Representations, p-adic Representations, Iwasawa Theory, p-adic Hodge Theory, Perfectoid Modular Curves, Overconvergent Modular Forms, Categorical Traces, Topos Theory, Groupoid Schemes, Cohomological Descent, Étale Cohomology, Grothendieck Topologies, Crystals, F-isocrystals, Shtukas, Stacky Picard Group, Robert Langlands, Pierre Deligne, Jean-Pierre Serre, Michael Harris, Richard Taylor, Vincent Lafforgue, Laurent Fargues, Peter Scholze, Rapoport, Zink, Carayol, Laumon, Waldspurger, Drinfeld, Gauge Theory, Topological Sigma Models, Electric–Magnetic Duality, String Theory, Branes, A-model, B-model, Quantum Geometric Langlands, Conformal Field Theory, Arithmetic Topology, Categorified Langlands Program, Extended Langlands Duality, Arithmetic Topos, Higher Reciprocity Laws, Functoriality Principle, Relative Trace Formula, Noncommutative Geometry, Motivic Integration, Crystalline Stacks, Langlands Program, Automorphic Forms, 11F70, 11F80, Shimura Varieties, Modular Forms, Representation Theory, Galois Representations

On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications

Συγγραφείς: Sekatskii, S. K.^Aff4

Συνεισφορές: Albeverio, Sergio, editor^Aff1, Balslev, Anindita, editor^Aff2, Weder, Ricardo, editor^Aff3

Πηγή: Schrödinger Operators, Spectral Analysis and Number Theory : In Memory of Erik Balslev. 348:241-254

Average values of L-functions in even characteristic: Average values of \(L\)-functions in even characteristic

Συγγραφείς: Hwanyup Jung, Sunghan Bae

Πηγή: Journal of Number Theory. 186:269-303

Θεματικοί όροι: Arithmetic theory of algebraic function fields, Mathematics - Number Theory, 11R11, 11R29, 11R42, 11R58, \(L\)-functions, FOS: Mathematics, Class numbers, class groups, discriminants, Zeta functions and \(L\)-functions of function fields, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT), 0101 mathematics, quadratic function fields, 01 natural sciences, class numbers

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/1701.01493
http://arxiv.org/abs/1701.01493
https://zbmath.org/7003395
https://doi.org/10.1016/j.jnt.2017.10.006
https://ui.adsabs.harvard.edu/abs/2017arXiv170101493B/abstract
https://www.sciencedirect.com/science/article/pii/S0022314X17303980

Note on the mean values of derivatives of quadratic Dirichlet L-functions in function fields: Note on the mean values of derivatives of quadratic Dirichlet \(L\)-functions in function fields

Συγγραφείς: Hwanyup Jung, Sunghan Bae

Πηγή: Finite Fields and Their Applications. 57:249-267

Θεματικοί όροι: hyperelliptic curves, Arithmetic theory of algebraic function fields, moments of \(L\)-functions, quadratic Dirichlet \(L\)-functions, Zeta functions and \(L\)-functions of function fields, derivatives of \(L\)-functions, 0101 mathematics, function fields, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dblp.uni-trier.de/db/journals/ffa/ffa57.html#BaeJ19
https://www.sciencedirect.com/science/article/pii/S1071579719300218
https://doi.org/10.1016/j.ffa.2019.02.010
https://koasas.kaist.ac.kr/handle/10203/261705

Quantum entanglement & purity testing: A graph zeta function perspective: Quantum entanglement \& purity testing: a graph zeta function perspective

Συγγραφείς: Zachary P. Bradshaw, Margarite L. LaBorde

Πηγή: Physics Letters A. 481:128993

Θεματικοί όροι: Extremal problems in graph theory, Entanglement measures, concurrencies, separability criteria, Quantum Physics, Quantum state spaces, operational and probabilistic concepts, Symmetric groups, graph theory, separability, FOS: Physical sciences, Mathematical Physics (math-ph), Singularities in algebraic geometry, quantum entanglement, functiograph zeta function, special functions, purity, Quantum coherence, entanglement, quantum correlations, Zeta functions and \(L\)-functions of function fields, Quantum Physics (quant-ph), Mathematical Physics

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2307.03321
https://zbmath.org/7722140
https://doi.org/10.1016/j.physleta.2023.128993

AVERAGE OF CLASS NUMBERS OF SOME FAMILY OF ARTIN-SCHREIER EXTENSIONS OF RATIONAL FUNCTION FIELDS: Average of class numbers of some family of Artin-Schreier extensions of rational function fields

Συγγραφείς: Hwanyup Jung

Πηγή: Korean Journal of Mathematics. 24:601-612

Θεματικοί όροι: Arithmetic theory of algebraic function fields, Artin-Schreier extensions, \(L\)-functions, Class numbers, class groups, discriminants, Zeta functions and \(L\)-functions of number fields, 0102 computer and information sciences, 0101 mathematics, Other abelian and metabelian extensions, 01 natural sciences, class numbers

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://society.kisti.re.kr/sv/SV_svpsbs03V.do?method=download&cn1=JAKO201610236162395
http://journal.kkms.org/index.php/kjm/article/view/462
https://journal.kkms.org/index.php/kjm/article/download/462/335
http://kkms.org/index.php/kjm/article/view/462
http://kkms.org/index.php/kjm/article/download/462/335

Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Συγγραφείς: Grenie', L., Molteni, G.

Πηγή: Funct. Approx. Comment. Math. 57, no. 1 (2017), 21-38

Θεματικοί όροι: 11R42: Zeta functions and $L$-functions of number fields, 11Y40: Algebraic number theory computations, Mathematics - Number Theory, explicit bounds, 16. Peace & justice, 01 natural sciences, Dedekind functions, GRH, 11R42 (Primary), 11Y70 (Secondary), prime ideal theorem, 11Y70, sharper bounds, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, 11R42

Περιγραφή αρχείου: application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/1312.4463
http://arxiv.org/pdf/1602.03515
http://arxiv.org/abs/1312.4463
http://arxiv.org/abs/1602.03515
https://dblp.uni-trier.de/db/journals/moc/moc85.html#GrenieM16
https://air.unimi.it/handle/2434/526913
https://ui.adsabs.harvard.edu/abs/2013arXiv1312.4463G/abstract
https://www.arxiv-vanity.com/papers/1602.03515/
https://128.84.21.199/abs/1602.03515
https://aisberg.unibg.it/handle/10446/102652
https://projecteuclid.org/journals/functiones-et-approximatio-commentarii-mathematici/volume-57/issue-1/Explicit-versions-of-the-prime-ideal-theorem-for-Dedekind-zeta/10.7169/facm/1611.full
https://hdl.handle.net/2434/448115
https://doi.org/10.1090/mcom3031
https://hdl.handle.net/10446/58029
https://doi.org/10.1090/mcom3031
https://projecteuclid.org/euclid.facm/1493949622

Explicit smoothed prime ideals theorems under GRH

Συγγραφείς: GRENIE, Loic Andre Henri, Molteni, Giuseppe

Πηγή: Mathematics of Computation. 85:1875-1899

Θεματικοί όροι: 11R42: Zeta functions and $L$-functions of number fields, 11Y40: Algebraic number theory computations, Mathematics - Number Theory, FOS: Mathematics, algebra and number theory, applied mathematics, computational mathematics, Number Theory (math.NT), 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/1312.4465
http://arxiv.org/abs/1312.4465
https://www.ams.org/mcom/earlyview/#mcom3039

Verifying a p-adic abelian Stark conjecture at s=1: Verifying a \(p\)-adic abelian Stark conjecture at \(s=1\).

Συγγραφείς: Roblot, Xavier-François, Solomon, David

Συνεισφορές: Roblot, Xavier-François

Πηγή: Journal of Number Theory. 107:168-206

Θεματικοί όροι: computation, Algebra and Number Theory, Mathematics - Number Theory, Abelian Stark conjectures, Zeta functions and \(L\)-functions, \(L\)-functions, real quadratic fields, Algebraic number theory computations, 01 natural sciences, 11R42 (Primary) 11S80 (Secondary), FOS: Mathematics, p-adic zeta functions, Integral representations related to algebraic numbers, Galois module structure of rings of integers, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT), Stark conjecture, 0101 mathematics, \(p\)-adic \(L\)-functions, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

Περιγραφή αρχείου: application/pdf; application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/math/0210176
https://hal.science/hal-00863142v1
https://ui.adsabs.harvard.edu/abs/2002math.....10176R/abstract
https://core.ac.uk/display/23530128
http://math.univ-lyon1.fr/~roblot/resources/zetap2.pdf
https://hal.archives-ouvertes.fr/hal-00863142/document
https://www.sciencedirect.com/science/article/pii/S0022314X04000198
https://hal.archives-ouvertes.fr/hal-00863142

Zeta functions of integral representations of cyclic p-groups: Zeta functions of integral representations of cyclic \(p\)-groups.

Συγγραφείς: Christian Wittmann

Πηγή: Journal of Algebra. 274:271-308

Θεματικοί όροι: Zeta function, \(p\)-adic representations of finite groups, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Algebra and Number Theory, Zeta functions and \(L\)-functions, integral representations, Modules over group rings, Structure theory of lattices, 01 natural sciences, Integral representations of finite groups, Möbius function, zeta functions, Integral representation, Zeta functions and \(L\)-functions of number fields, modules over group rings, 0101 mathematics, Möbius functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/abs/pii/S0021869303004228
https://www.sciencedirect.com/science/article/pii/S0021869303004228

Mean values of derivatives of $L$-functions in function fields: IV: Mean values of derivatives of \(L\)-functions in function fields. IV

Συγγραφείς: Andrade, Julio, Jung, Hwanyup

Θεματικοί όροι: Mathematics - Number Theory, moments of \(L\)-functions, quadratic Dirichlet \(L\)-functions, derivatives of \(L\)-functions, Zeta and \(L\)-functions in characteristic \(p\), random matrix theory, 11M38, 11M06, 11G20, 11M50, 14G10, function fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Curves over finite and local fields, Relations with random matrices, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Zeta functions and \(L\)-functions of function fields, Number Theory (math.NT)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1906.10373
https://zbmath.org/7481746
https://doi.org/10.4134/jkms.j210243

The value distribution of Artin L-series and zeros of Zeta-functions: The value distribution of Artin \(L\)-series and zeros of zeta-functions.

Συγγραφείς: Hartmut Bauer

Πηγή: Journal of Number Theory. 98:254-279

Θεματικοί όροι: Artin \(L\)-functions, Algebra and Number Theory, Zeta-functions, Zeta functions and \(L\)-functions, Zeta functions and \(L\)-functions of number fields, universality, zeta-functions, 0101 mathematics, Other Dirichlet series and zeta functions, Universality, 01 natural sciences, Artin L-functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/abs/pii/S0022314X02000483
https://www.sciencedirect.com/science/article/pii/S0022314X02000483

On the behavior of some two-variable p-adic L-functions: On the behavior of some two-variable \(p\)-adic \(L\)-functions.

Συγγραφείς: Paul Thomas Young

Πηγή: Journal of Number Theory. 98:67-88

Θεματικοί όροι: 03 medical and health sciences, Generalized Bernoulli polynomials, Algebra and Number Theory, 0302 clinical medicine, p-adic L-functions, Zeta functions and \(L\)-functions, Bernoulli polynomials, Kummer congruences, Zeta functions and \(L\)-functions of number fields, 0101 mathematics, Bernoulli and Euler numbers and polynomials, 01 natural sciences, \(p\)-adic \(L\)-functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1902868
https://doi.org/10.1016/s0022-314x(02)00031-8
http://www.sciencedirect.com/science/article/pii/S0022314X02000318
https://www.sciencedirect.com/science/article/pii/S0022314X02000318

On linear congruence relations for Kubota–Leopoldt 2-adic L-functions: On linear congruence relations for Kubota-Leopoldt 2-adic \(L\)-functions.

Συγγραφείς: Paul van Wamelen, Jerzy Urbanowicz

Πηγή: Journal of Number Theory. 98:195-216

Θεματικοί όροι: Vandermonde determinants, Algebra and Number Theory, 2-Adic L-functions, Generalized Vandermonde determinants, Zeta functions and \(L\)-functions, Class numbers, class groups, discriminants, Zeta functions of number fields, Congruences for special values of L-functions, Matrices, determinants in number theory, 01 natural sciences, Quadratic extensions, 0103 physical sciences, Zeta functions and \(L\)-functions of number fields, 0101 mathematics, quadratic fields, class numbers, \(p\)-adic \(L\)-functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/pii/S0022314X02000306
https://www.sciencedirect.com/science/article/abs/pii/S0022314X02000306

$p$-adic Abelian Stark conjectures at $s=1$: \(p\)-adic Abelian Stark conjectures at \(s=1\)

Συγγραφείς: Solomon, D

Πηγή: Annales de l’institut Fourier. 52:379-417

Θεματικοί όροι: special value, \(p\)-adic \(L\)-function, Zeta functions and \(L\)-functions, unit, abelian extension, regular, S-unit, 01 natural sciences, zeta-function, Integral representations related to algebraic numbers, Galois module structure of rings of integers, Zeta functions and \(L\)-functions of number fields, Stark conjecture, 0101 mathematics, totally real field

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.numdam.org/item/10.5802/aif.1891.pdf
https://zbmath.org/1794803
https://doi.org/10.5802/aif.1891
http://www.numdam.org/item/10.5802/aif.1891.pdf
https://eudml.org/doc/115984
https://aif.centre-mersenne.org/article/AIF_2002__52_2_379_0.pdf
http://math.univ-lyon1.fr/~roblot/resources/zetap1.pdf
https://aif.centre-mersenne.org/item/AIF_2002__52_2_379_0/
http://www.numdam.org/item/AIF_2002__52_2_379_0/

On optimal linear congruences for $L_2(k,\chi \omega ^{1-k})$: On optimal linear congruences for \(L_2(k,\chi\omega^{1-k})\)

Συγγραφείς: Urbanowicz, Jerzy

Πηγή: Publicationes Mathematicae Debrecen. 56:677-711

Θεματικοί όροι: Coleman's multilogarithms, Zeta functions and \(L\)-functions, special values of \(L\)-functions, Class numbers, class groups, discriminants, Zeta functions and \(L\)-functions of number fields, class number congruences, divisibility, 0101 mathematics, 2-adic \(L\)-functions, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1528689

Artin–Schreier extensions of the rational function field: Artin-Schreier extensions of the rational function field

Συγγραφείς: Bae, S Bae, Sunghan, Jung, H Jung, Hwanyup, Kang, PL Kang, Pyung-Lyun

Πηγή: Mathematische Zeitschrift. 276:613-633

Θεματικοί όροι: AVERAGE VALUES, L-SERIES, Arithmetic theory of algebraic function fields, \(L\)-functions, 4. Education, 0103 physical sciences, Class numbers, class groups, discriminants, orders, Zeta functions and \(L\)-functions of number fields, 0101 mathematics, 16. Peace & justice, Other abelian and metabelian extensions, 01 natural sciences, Artin-Schrier extensions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/6304085
https://doi.org/10.1007/s00209-013-1215-0
https://koasas.kaist.ac.kr/handle/10203/188873
https://link.springer.com/article/10.1007/s00209-013-1215-0