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arXiv · 1804.09892

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

Moni Kumari·M. Ram Murty
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Abstract

In this article, 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 $f$ and $g$ with Fourier coefficients $a_n$ and $b_n$ respectively, we consider the following questions: existence of infinitely many primes $p$ such that $a_p b_p\neq 0$; simultaneous non-vanishing in the short intervals and in arithmetic progressions; simultaneous sign changes in short intervals.

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Moni Kumari, M. Ram Murty. 2018-04-26. Simultaneous non-vanishing and sign changes of Fourier coefficients of modular forms. https://arxiv.org/abs/1804.09892

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