Quantum Drinfeld modules and ray class fields of real quadratic global function fields

Authors: L. Demangos, T. M. Gendron

Source: Research in the Mathematical Sciences. 12

Subject Terms: Modular and automorphic functions, quantum Drinfeld module, Arithmetic theory of algebraic function fields, function field arithmetic, Mathematics - Number Theory, Totally real fields, FOS: Mathematics, ray class field, Diophantine approximation in probabilistic number theory, Number Theory (math.NT), 0101 mathematics, Class field theory, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/abs/1709.05337
https://zbmath.org/8037122
https://doi.org/10.1007/s40687-025-00515-9

Curves with many rational points via Atkin–Lehner involution: Curves with many rational points via Atkin-Lehner involution

Authors: Vural Cam, Ferruh Özbudak

Source: Boletín de la Sociedad Matemática Mexicana. 31

Subject Terms: Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Atkin-Lehner involution, curves with many rational points, Drinfeld modular curves

File Description: application/xml

Access URL: https://zbmath.org/8037493
https://doi.org/10.1007/s40590-025-00746-4

Geometric main conjectures in function fields

Authors: Bley, Werner, Popescu, Cristian D.

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

Subject Terms: 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

File Description: application/xml

Access URL: http://arxiv.org/abs/2209.02440

Modular invariant of rank 1 Drinfeld modules and class field generation

Authors: L. Demangos, T.M. Gendron

Source: Journal of Number Theory. 237:40-66

Subject Terms: modular invariant, explicit class field theory, Arithmetic theory of algebraic function fields, Mathematics - Number Theory, FOS: Mathematics, Modular forms associated to Drinfel'd modules, Number Theory (math.NT), Drinfel'd modules, higher-dimensional motives, etc, 0101 mathematics, Class field theory, global function fields, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/pdf/2009.11750
http://arxiv.org/abs/2009.11750
https://www.sciencedirect.com/science/article/pii/S0022314X20303279

Inhomogeneous discriminant form equations and integral elements with given discriminant over finitely generated integral domains

Authors: Gaál, I.

Source: Publicationes Mathematicae Debrecen. 34:109-122

Subject Terms: finitely generated integral domains, inhomogeneous case, Multiplicative and norm form equations, Arithmetic theory of algebraic function fields, inhomogeneous discriminant form equations, 0101 mathematics, 01 natural sciences, effective bounds

File Description: application/xml

Access URL: https://zbmath.org/4016994

A note on the mean value of L(12,χ) in the real hyperelliptic ensemble: A note on the mean value of \(L(\frac{1}{2}, \chi)\) in the real hyperelliptic ensemble

Authors: Hwanyup Jung

Source: Journal of Number Theory. 211:477-499

Subject Terms: Curves over finite and local fields, Arithmetic theory of algebraic function fields, Cyclotomic extensions, 0103 physical sciences, moments of \(L\)-functions, quadratic Dirichlet \(L\)-functions, finite fields, 0101 mathematics, global function fields, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7185519
https://doi.org/10.1016/j.jnt.2019.10.018
https://www.sciencedirect.com/science/article/pii/S0022314X19303907

Several expressions of truncated Bernoulli-Carlitz and truncated Cauchy-Carlitz numbers

Authors: Takao Komatsu, Wenpeng Zhang

Source: AIMS Mathematics, Vol 5, Iss 6, Pp 5939-5954 (2020)

Subject Terms: recurrence relations, Exact enumeration problems, generating functions, Determinants, permanents, traces, other special matrix functions, hypergeometric bernoulli numbers, Cauchy-Carlitz numbers, 01 natural sciences, hypergeometric Cauchy numbers, truncated Bernoulli-Carlitz numbers, QA1-939, bernoulli-carlitz numbers, 0101 mathematics, Arithmetic theory of polynomial rings over finite fields, truncated Cauchy-Carlitz numbers, truncated bernoulli-carlitz numbers, Combinatorial identities, bijective combinatorics, Arithmetic theory of algebraic function fields, hypergeometric Bernoulli numbers, determinants, continued fractions, cauchy-carlitz numbers, function fields, Bernoulli-Carlitz numbers, truncated cauchy-carlitz numbers, Bernoulli and Euler numbers and polynomials, hypergeometric cauchy numbers, Mathematics

File Description: application/xml

Access URL: https://doaj.org/article/c49e972c55df4d7f86b3052ed278c3d7
https://www.aimspress.com/article/10.3934/math.2020380

Recent developments in the theory of multiple zeta values in positive characteristic

Authors: Ngo Dac, Tuan

Contributors: Ngo Dac, Tuan, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Excellence Research Chair FLCarPA supported by the Normandy Region, Research Institute for Mathematical Sciences, an International Joint Usage/Research Center, Kyoto University, Max Planck Institute for Mathematics, Bonn, ANR-19-CE40-0015,COLOSS,Cohomologie des espaces localement symétriques(2019)

Subject Terms: Hopf algebras, arithmetic theory of algebraic function fields, zeta and L-functions in characteristic p, [MATH] Mathematics [math], [MATH]Mathematics [math], multiple zeta values

File Description: application/pdf

Access URL: https://hal.science/hal-04396897v1

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

Authors: Hwanyup Jung, Sunghan Bae

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Οn zeta and multizeta values in pοsitive characteristic ; Sur les valeurs zêta et multizêta en caractéristique pοsitive

Authors: Le, Khac Nhuan

Contributors: Normandie, Ngo Dac, Tuan

Subject Terms: Valeurs zêta multiples, Valeurs zêta multiples de Pellarin, Valeurs zêta multiples triviales, Polylogarithmes multiples, Théorie arithmétique des corps de fonctions algébriques, Multiple zeta values, Pellarin’s multiple zeta values, Trivial multiple zeta values, Multiple polylogarithms, Arithmetic theory of algebraic function fields

Relation: http://www.theses.fr/2025NORMC209/document

Availability: http://www.theses.fr/2025NORMC209/document

On a Conjecture of Gezmis and Pellarin

Authors: Le, Khac Nhuan, Nguyen, Kien Huu

Contributors: Laboratoire de Mathématiques Nicolas Oresme (LMNO), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Chaire d'Excellence FLCarPA (Région Normandie)

Source: https://hal.science/hal-04138503 ; 2023.

Subject Terms: multiple zeta values, Pellarin's multiple zeta values, trivial multiple zeta values, multiple polylogarithms, arithmetic theory of algebraic function fields, [MATH]Mathematics [math]

Availability: https://hal.science/hal-04138503
https://hal.science/hal-04138503v1/document
https://hal.science/hal-04138503v1/file/On%20a%20Conjecture%20of%20Gezmis%20and%20Pellarin.pdf

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

Authors: Hwanyup Jung, Sunghan Bae

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Class number parities of compositum of quadratic function fields

Authors: Hwanyup Jung, Sunghan Bae

Source: Mathematica Slovaca. 67:305-320

Subject Terms: Arithmetic theory of algebraic function fields, compositum of quadratic function fields, Class numbers, class groups, discriminants, class number parities, 0101 mathematics, Other abelian and metabelian extensions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6725881
https://doi.org/10.1515/ms-2016-0268
http://www.degruyter.com/view/j/ms.2017.67.issue-2/ms-2016-0268/ms-2016-0268.xml

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

Authors: Hwanyup Jung

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Thue equations over algebraic function fields

Authors: Guenter Lettl

Source: Acta Arithmetica. 117:107-123

Subject Terms: Arithmetic theory of algebraic function fields, arithmetic theory of algebraic function fields, Thue-Mahler equations, Rational points, Cubic and quartic Diophantine equations, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/82829?download.pdf
https://zbmath.org/2169961
https://doi.org/10.4064/aa117-2-1
https://eudml.org/doc/278280
http://journals.impan.pl/cgi-bin/doi?aa117-2-1
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/117/2/82829/thue-equations-over-algebraic-function-fields
https://ui.adsabs.harvard.edu/abs/2005AcAri.117..107L/abstract

Some applications of Hasse principle for pseudoglobal fields

Authors: Andriychuk, V.

Subject Terms: Hasse principle, Arithmetic theory of algebraic function fields, Quadratic forms over global rings and fields, 0101 mathematics, Class field theory, 01 natural sciences, algebraic function field, quadratic form

File Description: application/xml

Access URL: https://zbmath.org/2169369
http://dspace.nbuv.gov.ua/handle/123456789/156462

Integral closures and weight functions over finite fields: Integral closures and weight functions over finite fields.

Authors: Ruud Pellikaan, Douglas A. Leonard

Source: Finite Fields and Their Applications. 9:479-504

Subject Terms: Towers of function fields, Algebra and Number Theory, Arithmetic theory of algebraic function fields, Applied Mathematics, Integral closure, 02 engineering and technology, Integral closure of commutative rings and ideals, 01 natural sciences, Structure theory for finite fields and commutative rings (number-theoretic aspects), AG codes, Theoretical Computer Science, Normalization, Weight function, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Engineering(all), Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: http://www.win.tue.nl/~ruudp/paper/42.pdf
https://research.tue.nl/en/publications/81c782b0-f318-4adf-af3d-007b35103168
https://doi.org/10.1016/S1071-5797(03)00038-8
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2Faae4cbcd-d1f2-40eb-916c-3673eccf4488
https://ieeexplore.ieee.org/document/1023331/
https://www.win.tue.nl/~ruudp/paper/42.pdf
https://www.sciencedirect.com/science/article/abs/pii/S1071579703000388
https://www.sciencedirect.com/science/article/pii/S1071579703000388
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2F81c782b0-f318-4adf-af3d-007b35103168

NOTE ON AVERAGE OF CLASS NUMBERS OF CUBIC FUNCTION FIELDS: Note on average of class numbers of cubic function fields

Authors: Hwanyup Jung

Source: Korean Journal of Mathematics. 22:419-427

Subject Terms: Arithmetic theory of algebraic function fields, Cubic and quartic extensions, cubic function field, Class numbers, class groups, discriminants, average of class numbers, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://www.ndsl.kr/soc_img/society/kkms/E1KKMK/2014/v22n3/E1KKMK_2014_v22n3_419.pdf
https://zbmath.org/7173058
https://doi.org/10.11568/kjm.2014.22.3.419
http://journal.kkms.org/index.php/kjm/article/view/292/205
https://journal.kkms.org/index.php/kjm/article/download/292/205
http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1KKMK_2014_v22n3_419
http://kkms.org/index.php/kjm/article/download/292/205
http://kkms.org/index.php/kjm/article/view/292

A note on the mean value of L(1, χ) in the hyperelliptic ensemble: A note on the mean value of \(L(1, \chi)\) in the hyperelliptic ensemble

Authors: Hwanyup Jung

Source: International Journal of Number Theory. 10:859-874

Subject Terms: class number, function field, Arithmetic theory of algebraic function fields, Cyclotomic extensions, Class numbers, class groups, discriminants, 0101 mathematics, 16. Peace & justice, finite field, 01 natural sciences, mean values of \(L\)-functions, 3. Good health

File Description: application/xml

Access URL: https://www.worldscientific.com/doi/abs/10.1142/S1793042114500031

HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS: Hilbert \(2\)-class field towers of real quadratic function fields

Authors: Hwan-Yup Jung

Source: Communications of the Korean Mathematical Society. 29:219-226

Subject Terms: Quadratic extensions, function field, density, Arithmetic theory of algebraic function fields, Hilbert class field, 0101 mathematics, 01 natural sciences, class field tower

File Description: application/xml

Access URL: http://www.ndsl.kr/soc_img/society/kms/DBSHCJ/2014/v29n2/DBSHCJ_2014_v29n2_219.pdf
https://zbmath.org/6301787
https://doi.org/10.4134/ckms.2014.29.2.219
http://koreascience.or.kr/journal/view.jsp?kj=DBSHCJ&py=2014&vnc=v29n2&sp=219
http://www.ndsl.kr/soc_img/society/kms/DBSHCJ/2014/v29n2/DBSHCJ_2014_v29n2_219.pdf