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A generalized Davenport expansion

Part of: Harmonic analysis in one variable Zeta and $L$-functions: analytic theory Exponential sums and character sums

Published online by Cambridge University Press:  26 August 2021

Alexander E. Patkowski
Alexander E. Patkowski*
Affiliation:
1390 Bumps River Rd., Centerville, MA02632, USA (alexpatk@hotmail.com, alexepatkowski@gmail.com)
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Abstract

We prove a new generalization of Davenport's Fourier expansion of the infinite series involving the fractional part function over arithmetic functions. A new Mellin transform related to the Riemann zeta function is also established.

Keywords

Davenport expansionsRiemann zeta functionFourier series

MSC classification

Primary: 11L20: Sums over primes 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 3 , August 2021 , pp. 711 - 715
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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