An exact renormalization formula for Gaussian exponential sums and applications
Alexander Fedotov, Fr\'ed\'eric Klopp (LAGA)
TL;DR
This paper derives an exact renormalization formula for Gaussian exponential sums, enabling precise analysis of their growth behavior, with potential applications in number theory and related fields.
Contribution
It introduces a Hardy-Littlewood style renormalization formula with an exact remainder term for Gaussian exponential sums, advancing analytical techniques in this area.
Findings
Derived an exact renormalization formula for Gaussian exponential sums
Described the typical growth behavior of these sums
Provided potential applications in number theory
Abstract
In the present paper, we derive a renormalization formula "\`a la Hardy-Littlewood" for the Gaussian exponential sums with an exact formula for the remainder term. We use this formula to describe the typical growth of the Gaussian exponential sums.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Harmonic Analysis Research