Výsledky vyhledávání - "11B65, 11F27"

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New fifth and seventh order mock theta function identities

Autor: Garvan, Frank

We give simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan fifth order mock theta functions $\chi_0(q)$ and $\chi_1(q)$ and all three of Ramanujan's seventh order mock theta functions. We find that the coeff

Externí odkaz: http://arxiv.org/abs/1907.04803

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Four identities related to third order mock theta functions

Autor: Cui, Su-Ping, Gu, Nancy S. S., Su, Chen-Yang

Ramanujan presented four identities for third order mock theta functions in his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first proved these four identities. Recently, Andrews et al. provided different proofs by using $q$-se

Externí odkaz: http://arxiv.org/abs/1812.00213

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A Kronecker-type identity and the representations of a number as a sum of three squares

Autor: Mortenson, Eric T.

Publikováno v: Bulletin of the London Mathematical Society, 49 (2017), no. 5, 770-783

By considering a limiting case of a Kronecker-type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews-Crandall identity to give a new proof of a formula of Gauss for the representations of a number as a sum of

Externí odkaz: http://arxiv.org/abs/1702.01627

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A double-sum Kronecker-type identity

Autor: Mortenson, Eric T.

Publikováno v: Advances in Applied Mathematics, 82 (2017), 155-177

We prove a double-sum analog of an identity known to Kronecker and then express it in terms of functions studied by Appell and Kronecker's student Lerch, in so doing we show that the double-sum analog is of mixed mock modular form. We also give relat

Externí odkaz: http://arxiv.org/abs/1601.01913

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Ramanujan's radial limits and mixed mock modular bilateral $q$-hypergeometric series

Autor: Mortenson, Eric

Publikováno v: Proceedings of the Edinburgh Mathematical Society, (2) 59 (2016), no. 3, pp. 787-799

Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom, Ono, and Rhoades for mock theta functions. Here we see that the author's previous work on the dual nature of Appell--Lerch sum

Externí odkaz: http://arxiv.org/abs/1309.4162

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A note on a generalized circular summation formula of theta functions

Autor: Zhu, Jun-Ming

In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes for a type of generalized cubic theta functions.
Comment: 5 page

Externí odkaz: http://arxiv.org/abs/1202.1869

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K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products

Autor: Berkovich, Alexander, Garvan, Frank G.

We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function

Externí odkaz: http://arxiv.org/abs/math/0702027

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A heuristic guide to evaluating triple-sums

Autor: Mortenson, Eric

Publikováno v: Hardy-Ramanujan Journal
Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Volume 43-Special Commemorative volume in honour of Srinivasa Ramanujan, pp.99-121

Using a heuristic that relates Appell--Lerch functions to divergent partial theta functions one can expand Hecke-type double-sums in terms of Appell--Lerch functions. We give examples where the heuristic can be used as a guide to evaluate analogous t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98becc4d62739bcac2dd25f6099f50f1
https://doi.org/10.46298/hrj.2021.7431