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Singular moduli and the distribution of partition ranks modulo 2

Published online by Cambridge University Press:  18 December 2015

RIAD MASRI
RIAD MASRI*
Affiliation:
Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843-3368, U.S.A. e-mail: [email protected]
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Abstract

In this paper, we prove an asymptotic formula with a power saving error term for traces of weight zero weakly holomorphic modular forms of level N along Galois orbits of Heegner points on the modular curve X0(N). We use this result to study the distribution of partition ranks modulo 2. In particular, we give an asymptotic formula with a power saving error term for the number of partitions of a positive integer n with even (respectively, odd) rank. We use these results to deduce a strong quantitative form of equidistribution of partition ranks modulo 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 2 , March 2016 , pp. 209 - 232
Copyright
Copyright © Cambridge Philosophical Society 2015 

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