Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms

Moni Kumari, M. Ram Murty

Type: Article

Publication Date: 2018-05-22

Citations: 10

DOI: https://doi.org/10.1142/s1793042118501397

Abstract

In this paper, we give some results on simultaneous non-vanishing and simultaneous sign-changes for the Fourier coefficients of two modular forms. More precisely, given two modular forms [Formula: see text] and [Formula: see text] with Fourier coefficients [Formula: see text] and [Formula: see text] respectively, we consider the following questions: existence of infinitely many primes [Formula: see text] such that [Formula: see text]; simultaneous non-vanishing in the short intervals and in arithmetic progressions; simultaneous sign changes in short intervals.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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