Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Distribution of Coefficients of Modular Forms and the Partition Function (1102.4400v2)

Published 22 Feb 2011 in math.NT

Abstract: Let $\ell\ge5$ 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 $1\le r\le\ellj$, $$\sharp{1\le n\le X\ |\ p(n)\equiv r\pmod{\ellj}}\gg_{s,r,\ellj}\frac{\sqrt X}{\log X}(\log\log X)s.$$

Summary

We haven't generated a summary for this paper yet.