Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

Scott Ahlgren; K. I.M. Byungchan

doi:10.1017/S0305004114000565

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

Scott Ahlgren, K. I.M. Byungchan

School of Natural Sciences

University of Illinois

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that the coefficients of the mock theta functions (Formula Presented) possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function.

Original language	English
Pages (from-to)	111-129
Number of pages	19
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	158
Issue number	1
DOIs	https://doi.org/10.1017/S0305004114000565
State	Published - 20 Jan 2015

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title = "Mock theta functions and weakly holomorphic modular forms modulo 2 and 3",

abstract = "We prove that the coefficients of the mock theta functions (Formula Presented) possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function.",

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AB - We prove that the coefficients of the mock theta functions (Formula Presented) possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function.

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Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

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