TRANSFORMATION AND SYMMETRIES FOR THE ANDREWS-GARVAN CRANK FUNCTION: Transformation and symmetries for the Andrews-Garvan crank function

Συγγραφείς: Sarma, Rishabh

Πηγή: Hardy-Ramanujan Journal.

Θεματικοί όροι: Dyson's rank function, Mathematics - Number Theory, crank function, modular forms, 01 natural sciences, 05A19, 11B65, 11F11, 11F37, 11P82, 11P83, 33D15, Partitions, congruences and congruential restrictions, Binomial coefficients, factorials, \(q\)-identities, partitions, FOS: Mathematics, Analytic theory of partitions, Number Theory (math.NT), 0101 mathematics, Holomorphic modular forms of integral weight, Forms of half-integer weight, nonholomorphic modular forms, Combinatorial identities, bijective combinatorics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2301.10991

Strange and pseudo-differentiable functions with applications to prime partitions

Συγγραφείς: Anji Dong, Nicolas Robles, Alexandru Zaharescu, Dirk Zeindler

Πηγή: Research in Number Theory. 11

Θεματικοί όροι: weights associated to partitions, Mathematics - Number Theory, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, Estimates on exponential sums, von Mangoldt function, zeros of zeta function, strange functions, Hardy-Littlewood circle method, Applications of the Hardy-Littlewood method, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\), Riemann and other hypotheses, Primary: 11P55, 11P82, 26A24. Secondary: 11L07, 11L20, 11M26, pseudo-differentiable functions, FOS: Mathematics, Analytic theory of partitions, inclusion-exclusion, Number Theory (math.NT), exponential sums, Sums over primes

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2412.20102
https://zbmath.org/8034695
https://doi.org/10.1007/s40993-025-00628-8

Zeros of Hook Polynomials and Related Questions: Zeros of hook polynomials and related questions

Συγγραφείς: Bridges, Walter, Craig, William, Folsom, Amanda, Rolen, Larry

Πηγή: Symmetry, Integrability and Geometry: Methods and Applications.

Θεματικοί όροι: Combinatorial aspects of partitions of integers, zeros of polynomials, Mathematics - Number Theory, Exact enumeration problems, generating functions, theta functions, hook length, integer partitions, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), zero attractor, FOS: Mathematics, Mathematics - Combinatorics, Analytic theory of partitions, Theta series, Weil representation, theta correspondences, asymptotic behavior, Combinatorics (math.CO), Number Theory (math.NT)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2408.16902
https://zbmath.org/8035728
https://doi.org/10.3842/sigma.2025.026

Vanishing properties of Kloosterman sums and Dyson’s conjectures: Vanishing properties of Kloosterman sums and Dyson's conjectures

Συγγραφείς: Sun, Qihang

Πηγή: The Ramanujan Journal. 66

Θεματικοί όροι: Partitions, congruences and congruential restrictions, Dyson's rank, Mathematics - Number Theory, Rademacher exact formula, 11L05, 11P83, 11P82, FOS: Mathematics, Analytic theory of partitions, Kloosterman sum, Number Theory (math.NT), Gauss and Kloosterman sums, generalizations, integer partition

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2406.07469

The restricted partition and q-partial fractions: The restricted partition and \(q\)-partial fractions

Συγγραφείς: N. Uday Kiran

Πηγή: Research in Number Theory. 9

Θεματικοί όροι: Mathematics - Number Theory, degenerate numbers, Exact enumeration problems, generating functions, Elementary theory of partitions, Sylvester waves, Ramanujan sum, cyclotomic polynomials, 01 natural sciences, 05A15, 11P82, 11B68, FOS: Mathematics, Analytic theory of partitions, Number Theory (math.NT), 0101 mathematics, Bernoulli and Euler numbers and polynomials, restricted partition

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2202.03603
https://zbmath.org/7735439
https://doi.org/10.1007/s40993-023-00468-4

Partitions: At the Interface of q-Series and Modular Forms: Partitions: At the interface of \(q\)-series and modular forms

Συγγραφείς: George E. Andrews

Πηγή: Developments in Mathematics ISBN: 9781441953957

Θεματικοί όροι: Basic hypergeometric functions in one variable, \({}_r\phi_s\), Rademacher conjecture, partitions, Analytic theory of partitions, Elementary theory of partitions, modular forms, mock theta functions, 0101 mathematics, q-series, Holomorphic modular forms of integral weight, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2022039
https://doi.org/10.1023/a:1026224002193
https://link.springer.com/article/10.1023/A:1026224002193
https://pennstate.pure.elsevier.com/en/publications/partitions-at-the-interface-of-q-series-and-modular-forms
https://rd.springer.com/chapter/10.1007/978-1-4757-6044-6_27

On the Asymptotic Behaviour of General Partition Functions, II: On the asymptotic behaviour of general partition functions. II

Συγγραφείς: Jean-Louis Nicolas, András Sárközy

Πηγή: Developments in Mathematics ISBN: 9781441953957

Θεματικοί όροι: partitions, generating functions, Analytic theory of partitions, Elementary theory of partitions, asymptotic results, asymptotic estimate, number of partitions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/content/pdf/10.1007%2F978-1-4757-6044-6_21.pdf
http://math.univ-lyon1.fr/~nicolas/asympbehav2.pdf
https://link.springer.com/article/10.1023/A%3A1009821821206
https://rd.springer.com/chapter/10.1007/978-1-4757-6044-6_21

A generalized formula of Hardy

Συγγραφείς: Geoffrey B. Campbell

Πηγή: International Journal of Mathematics and Mathematical Sciences, Vol 17, Iss 2, Pp 369-378 (1994)

Θεματικοί όροι: combinatorial inequalities, Combinatorial aspects of partitions of integers, Farey sequences, analytic theory of partitions, partitions of integers, Combinatorial inequalities, 01 natural sciences, the sequences \(1^k, 2^k, \dots\), 0104 chemical sciences, combinatorial identities, Fractals, fractals, QA1-939, formula of Hardy, Analytic theory of partitions, 0101 mathematics, Mathematics, identity, partition of numbers

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://downloads.hindawi.com/journals/ijmms/1994/979718.pdf
https://zbmath.org/569406
https://doi.org/10.1155/s0161171294000517
https://doaj.org/article/d427f5e1278d4834b884262650215d43
https://www.hindawi.com/journals/ijmms/1994/979718/reprint/
https://downloads.hindawi.com/journals/ijmms/1994/979718.pdf
http://downloads.hindawi.com/journals/ijmms/1994/979718.pdf
https://www.hindawi.com/journals/ijmms/1994/979718/
https://eudml.org/doc/46967

On the representation of integers as sums of triangular numbers

Συγγραφείς: Ono, Ken, Robins, Sinai, Wahl, P.T.

Πηγή: Aggregating clones, colors, equations, iterates, numbers, and tiles ISBN: 9783764352431

Θεματικοί όροι: representation of integers, 4. Education, modular forms, sums of triangular numbers, 01 natural sciences, Article, number of lattice points in a \(k\)-dimensional sphere, 510.mathematics, Lattice points in specified regions, Lattices and convex bodies (number-theoretic aspects), 24-dimensional Leech lattices, Analytic theory of partitions, survey, Ramanujan's function, 0101 mathematics, Holomorphic modular forms of integral weight

Περιγραφή αρχείου: application/xml; image/jpeg; application/pdf

Σύνδεσμος πρόσβασης: https://eudml.org/doc/137621
https://link.springer.com/article/10.1007%2FBF01831114
https://rd.springer.com/chapter/10.1007/978-3-0348-9096-0_6

Arithmetic Properties of Summands of Partitions II: Arithmetic properties of summands of partitions. II

Συγγραφείς: András Sárközy, Cécile Dartyge

Πηγή: The Ramanujan Journal. 10:383-394

Θεματικοί όροι: Analytic theory of partitions, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://hal.archives-ouvertes.fr/hal-00091844/file/partsfc.pdf
https://hal.archives-ouvertes.fr/hal-00091844
https://link.springer.com/article/10.1007/s11139-005-4855-9
https://hal.archives-ouvertes.fr/hal-00091844/document
https://link.springer.com/content/pdf/10.1007%2Fs11139-005-4855-9.pdf

On the Coincidence of Limit Shapes for Integer Partitions and Compositions, and a Slicing of Young Diagrams: On the coincidence of limit shapes of partitions and compositions, and a slicing of Young diagrams

Συγγραφείς: Yu. V. Yakubovich

Πηγή: Journal of Mathematical Sciences. 131:5569-5577

Θεματικοί όροι: Combinatorial aspects of partitions of integers, Combinatorial probability, Combinatorial aspects of representation theory, Analytic theory of partitions, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1007/s10958-005-0427-1

Identities of the Rogers–Ramanujan–Bailey type: Identities of the Rogers-Ramanujan-Bailey type

Συγγραφείς: Andrew V. Sills

Πηγή: Journal of Mathematical Analysis and Applications. 308:669-688

Θεματικοί όροι: Rogers-Ramanujan identities, \(q\)-series identities, Applied Mathematics, basic hypergeometric series, 11B65 33D15 05A19, 01 natural sciences, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bailey pairs, Analytic theory of partitions, 0101 mathematics, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1812.04459
http://ui.adsabs.harvard.edu/abs/2005JMAA..308..669S/abstract
https://works.bepress.com/andrew_sills/112/
https://www.sciencedirect.com/science/article/pii/S0022247X04010145#!
https://arxiv.org/abs/1812.04459
https://www.sciencedirect.com/science/article/pii/S0022247X04010145
https://www.sciencedirect.com/science/article/abs/pii/S0022247X04010145

A probabilistic approach to analytic arithmetic on algebraic function fields

Συγγραφείς: Arratia, R, Barbour, A D, Tavaré, S

Συνεισφορές: University of Zurich, Arratia, R

Πηγή: Mathematical Proceedings of the Cambridge Philosophical Society. 139:1-26

Θεματικοί όροι: 10123 Institute of Mathematics, 510 Mathematics, Combinatorial probability, Arithmetic functions in probabilistic number theory, Commutative semigroups, Central limit and other weak theorems, Analytic theory of partitions, 0101 mathematics, 01 natural sciences, 2600 General Mathematics

Περιγραφή αρχείου: application/xml; ZORA-21665V.pdf - application/pdf

Σύνδεσμος πρόσβασης: https://www.zora.uzh.ch/id/eprint/21665/1/ZORA-21665V.pdf
https://www.zora.uzh.ch/id/eprint/21665/1/ZORA-21665V.pdf
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/probabilistic-approach-to-analytic-arithmetic-on-algebraic-function-fields/CEA2C45BA3DB46B2F6B9BFB7F35D36E4
https://ui.adsabs.harvard.edu/abs/2005MPCPS.139....1A/abstract
https://www.zora.uzh.ch/id/eprint/21665/
https://www.zora.uzh.ch/id/eprint/21665/
https://doi.org/10.5167/uzh-21665

Applications of the Wulff construction to the number theory: Applications of the Wulff construction to number theory

Συγγραφείς: Shlosman, Senya

Συνεισφορές: Arxiv, Import

Πηγή: Journal of Mathematical Sciences. 126:1128-1132

Θεματικοί όροι: Combinatorial aspects of partitions of integers, 82B20, 05A17, FOS: Physical sciences, Mathematical Physics (math-ph), Asymptotic enumeration, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, Analytic theory of partitions, Combinatorics (math.CO), [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Mathematical Physics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/math-ph/0109027v1.pdf
http://arxiv.org/abs/math-ph/0109027
https://hal.science/hal-00117571v1
https://link.springer.com/content/pdf/10.1007/s10958-005-0108-0.pdf
https://link.springer.com/article/10.1007/s10958-005-0108-0
https://hal.archives-ouvertes.fr/hal-00117571

Cranks and dissections in Ramanujan's lost notebook

Συγγραφείς: Berndt, B.C., Chan, H.H., Chan, S.H., Liaw, W.-C.

Συνεισφορές: MATHEMATICS

Πηγή: Journal of Combinatorial Theory, Series A. 109:91-120

Θεματικοί όροι: Dissections, Ramanujan's lost notebook, Partition function p(n), congruences, 0102 computer and information sciences, Cranks, 01 natural sciences, Theoretical Computer Science, Partitions, congruences and congruential restrictions, Computational Theory and Mathematics, cranks, partitions, Discrete Mathematics and Combinatorics, Analytic theory of partitions, dissections, 0101 mathematics, Congruences for p(n)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2136714
https://doi.org/10.1016/j.jcta.2004.06.013
http://www.sciencedirect.com/science/article/pii/S0097316504001189
https://www.sciencedirect.com/science/article/abs/pii/S0097316504001189
https://experts.illinois.edu/en/publications/cranks-and-dissections-in-ramanujans-lost-notebook
https://www.sciencedirect.com/science/article/pii/S0097316504001189
http://www.math.nus.edu.sg/~chanhh/papers/41.pdf
https://core.ac.uk/display/82057099

String Jacobi Matrices with Very Fast Decreasing Weights: String Jacobi matrices with very fast decreasing weights

Συγγραφείς: Eduard Tur

Πηγή: Integral Equations and Operator Theory. 50:115-128

Θεματικοί όροι: asymptotic of eigenvalues, Jacobi (tridiagonal) operators (matrices) and generalizations, partitions, Special classes of entire functions of one complex variable and growth estimates, Analytic theory of partitions, continued fractions, 0101 mathematics, Hellinger-Weyl function, 01 natural sciences, Jacobi matrices, entire functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1007/s00020-002-1269-6

Multiplicity and Number of Parts in Overpartitions: Multiplicity and number of parts in overpartitions

Συγγραφείς: Corteel, Sylvie, Hitczenko, Paweł

Πηγή: Annals of Combinatorics. 8:287-301

Θεματικοί όροι: Combinatorial aspects of partitions of integers, Combinatorial probability, partitions, Analytic theory of partitions, 0102 computer and information sciences, combinatorial probability, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.math.drexel.edu/~phitczen/over.pdf
https://zbmath.org/2124597
https://doi.org/10.1007/s00026-004-0221-7
https://link.springer.com/article/10.1007/s00026-004-0221-7
https://link.springer.com/10.1007/s00026-004-0221-7
http://www.combinatorics.net/aoc/toc/V8n3/Corteel/8_3_287.pdf

On the Asymptotics of the Binary Partition Function: On the asymptotics of the binary partition function

Συγγραφείς: Protasov, Vladimir

Πηγή: Mathematical Notes. 76:144-149

Θεματικοί όροι: Combinatorial aspects of partitions of integers, asymptotics, binary partition function, binary expansion, Mathematics (all), Analytic theory of partitions, Rate of growth of arithmetic functions, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2121453
https://doi.org/10.1023/b:matn.0000036752.47140.98
https://link.springer.com/article/10.1023/B:MATN.0000036752.47140.98
https://link.springer.com/content/pdf/10.1023/B:MATN.0000036752.47140.98.pdf

Arithmetic Properties of Summands of Partitions: Arithmetic properties of summands of partitions

Συγγραφείς: Dartyge, Cécile, Sárközy, András

Πηγή: The Ramanujan Journal. 8:199-215

Θεματικοί όροι: residue classes, partitions, Analytic theory of partitions, 0102 computer and information sciences, 0101 mathematics, 16. Peace & justice, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://hal.archives-ouvertes.fr/hal-00130635/file/RevAdfixed.pdf
https://zbmath.org/2153727
https://doi.org/10.1023/b:rama.0000040481.02788.ae

Popularity of Sets Represented by the Partitions of n: Popularity of sets represented by the partitions of \(n\)

Συγγραφείς: Mihály Szalay, Jean-Louis Nicolas

Πηγή: The Ramanujan Journal. 8:147-175

Θεματικοί όροι: partitions, generating functions, Analytic theory of partitions, Elementary theory of partitions, 0102 computer and information sciences, 0101 mathematics, asymptotic estimate, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2153725
https://doi.org/10.1023/b:rama.0000040479.45507.7b
http://math.univ-lyon1.fr/~nicolas/szalay2.pdf
https://link.springer.com/article/10.1023%2FB%3ARAMA.0000040479.45507.7b