Exponential sums in prime fields for modular forms

2020/07/30 by Bajpai, Jitendra, Bhakta, Subham, Garcia, Victor C.
#11B37 #11F80 #11L07 #FOS: Mathematics #Number Theory (math.NT) #Primary 11F30 #Secondary 11P05

paper · doi:10.48550/arxiv.2007.15482

Abstract

The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on Shparlinski's bound for exponential sums attached to certain recurrence sequences over finite fields.

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• Exponential sums over singular binary quartic forms and applications
• Congruence classes for modular forms over small sets
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