Cesàro averages for Goldbach representations with summands in arithmetic progressions-Reference-Cited by-同舟云学术

Cesàro averages for Goldbach representations with summands in arithmetic progressions

Published:2021-07-06 Issue:10 Volume:17 Page:2379-2393
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Cantarini Marco¹,Gambini Alessandro²^ORCID,Zaccagnini Alessandro³

Affiliation:

1. Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italia

2. Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italia

3. Dipartimento di Scienze, Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area Delle Scienze 53/a, 43124 Parma, Italia

Abstract

Let [Formula: see text] be the von Mangoldt function, let [Formula: see text] be an integer and let [Formula: see text] be the counting function for the Goldbach numbers with summands in arithmetic progression modulo a common integer [Formula: see text]. We prove an asymptotic formula for the weighted average, with Cesàro weight of order [Formula: see text], with [Formula: see text], of this function. Our result is uniform in a suitable range for [Formula: see text].

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042121500937

Reference24 articles.

1. GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L ‐FUNCTIONS

2. Explicit formulae for averages of Goldbach representations

3. On the Cesàro average of the “Linnik numbers”

4. On the Cesàro average of the numbers that can be written as sum of a prime and two squares of primes

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