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A generalized Davenport expansion

Published online by Cambridge University Press:  26 August 2021

Alexander E. Patkowski*
Affiliation:
1390 Bumps River Rd., Centerville, MA02632, USA ([email protected], [email protected])

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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