A Generalized Davenport Expansion

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.

Corrected the first version

References in corpus (2)

• On some Definite Integrals involving the Hurwitz Zeta function
• On Popov's formula involving the Von Mangoldt function