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Explicit asymptotics for certain single and double exponential sums

Published online by Cambridge University Press:  22 January 2019

K. Kalimeris
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, UK (kk364@cam.ac.uk)
A. S. Fokas
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, UK and Viterbi School of Engineering, University of Southern California, Los Angeles, CA90089-2560, USA
Corresponding
E-mail address:

Abstract

By combining classical techniques together with two novel asymptotic identities derived in recent work by Lenells and one of the authors, 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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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References

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