New York Journal of Mathematics
Volume 20 (2014) 229-239


Sanoli Gun and M. Ram Murty

Divisors of Fourier coefficients of modular forms

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Published: March 14, 2014
Keywords: Divisor function, Fourier coefficients of modular forms, generalized Riemann hypothesis, Chebotarev density theorem
Subject: 11F30, 11N37

Let d(n) denote the number of divisors of n. In this paper, we study the average value of d(a(p)), where p is a prime and a(p) is the p-th Fourier coefficient of a normalized Hecke eigenform of weight k ≧ 2 for Γ0(N) having rational integer Fourier coefficients.


Research of the first author was partially supported by IMSc Number Theory grant. Research of the second author was partially supported by an NSERC Discovery grant.

Author information

Sanoli Gun:
Institute for Mathematical Sciences, CIT Campus, Taramani, Chennai, 600 113, India

M. Ram Murty:
Department of Mathematics, Queen's University, Kingston, Ontario, K7L 3N6, Canada.