Explicit asymptotics for certain single and double exponential sums

TL;DR

This paper develops explicit asymptotic formulas for specific single and double exponential sums, enhancing understanding of their behavior and applications to problems like the Lindelöf hypothesis.

Contribution

It introduces new asymptotic identities and applies classical techniques to analyze Riemann-zeta type sums and Euler-Zagier double sums for particular parameter ranges.

Findings

Derived explicit asymptotics for certain exponential sums

Analyzed Euler-Zagier double sums for specific parameters

Contributed to approaches addressing the Lindelöf hypothesis

Abstract

By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of $Re\{u\}$ and $Re\{v\}$ and for a variety of sets of summation, as well as particular cases of Mordell-Tornheim double sums. Some of these results are used in [F] where a novel approach to the Lindel\"of hypothesis is presented.