Distribution of Coefficients of Modular Forms and the Partition Function

2011/02/22 by Shi-Chao Chen, Chen, Shi-Chao
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1102.4400

Abstract

Let ℓ≥5 be an odd prime and j, s be positive integers. We study the distribution of the coefficients of integer and half-integral weight modular forms modulo odd positive integer M. As a consequence, we prove that for each integer 1≤ r≤ℓ^j, \sharp\1≤ n≤ X | p(n)≡ r\pmodℓ^j\≫_s,r,ℓ^j(√ X)/(log X)(loglog X)^s.

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