Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415588 | Journal of Number Theory | 2014 | 6 Pages |
Abstract
â¢We establish an estimate on the coefficients of the eigenforms.â¢Our result is related to the well known Lehmerʼs conjecture.â¢The combinatorial sieve is used in our proof.
Lehmerʼs conjecture on Ramanujanʼs tau function Ï(n) asserts that Ï(n)â 0 for any n⩾1. We consider a variant of Lehmerʼs conjecture. Let f(z)=ân=1âane2Ïinz be a normalized eigenform, where the an are rational integers for all n, and let g(n) be a polynomial with integer coefficients. We bound the number of n⩽x such that an and g(n) have no common factor.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shi-Chao Chen,