Proofs of some conjectures of Chan on Appell-Lerch sums

DOI10.1007/s11139-018-0076-xzbMath1450.11107arXiv1807.03957OpenAlexW2949541936WikidataQ113900585 ScholiaQ113900585MaRDI QIDQ2301906

Nilufar Mana Begum, Nayandeep Deka Baruah

Publication date: 25 February 2020

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03957

zbMATH Keywords

theta functioncongruencemock theta functionAppell-Lerch sum

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (2)

Proof of a conjectural congruence of Chan for Appell–Lerch sums ⋮ Proofs of conjectures of Chan for \(d(n)\)

Cites Work

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• On the dual nature of partial theta functions and Appell-Lerch sums
• Dyson's ranks and Appell-Lerch sums
• Ramanujan's ``Lost Notebook. VII: The sixth order mock theta functions
• Generalizations of some conjectures of Chan on congruences for Appell-Lerch sums
• Ramanujan's \(_1\psi_1\) summation, Hecke-type double sums, and Appell-Lerch sums
• Arithmetic properties for Appell-Lerch sums
• Transformation formula of the ``second order mock theta function
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• On certain explicit congruences for mock theta functions
• TWO CONGRUENCES FOR APPELL–LERCH SUMS
• Identities for Ramanujan's Sixth-Order Mock Theta Functions
• Exact generating functions for the number of partitions into distinct parts
• Congruences for Ramanujan's φ function

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