Preprint Article Version 1 This version is not peer-reviewed

Mellin Convolution and its Extensions, Perron Formula and Explicit Formulae

Version 1 : Received: 29 December 2017 / Approved: 3 January 2018 / Online: 3 January 2018 (05:07:10 CET)

How to cite: Garcia Moreta, J.J. Mellin Convolution and its Extensions, Perron Formula and Explicit Formulae. Preprints 2018, 2018010020 (doi: 10.20944/preprints201801.0020.v1). Garcia Moreta, J.J. Mellin Convolution and its Extensions, Perron Formula and Explicit Formulae. Preprints 2018, 2018010020 (doi: 10.20944/preprints201801.0020.v1).

Abstract

In this paper we use the Mellin convolution theorem, which is related to Perron's formula. Also we introduce new explicit formulae for arithmetic function which generalize the explicit formulae of Weil for other arithmetic functions different from the Von-Mangoldt function.

Subject Areas

Riemann-weil formula; perron formula; explicit formulae; Riemann zeros

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