Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Explicit formulae for averages of Goldbach representations

Authors: Jörg Brüdern, Jerzy Kaczorowski and Alberto Perelli
Journal: Trans. Amer. Math. Soc. 372 (2019), 6981-6999
MSC (2010): Primary 11P32, 11N05
Published electronically: March 20, 2019
MathSciNet review: 4024544
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an explicit formula, analogous to the classical explicit formula for $\psi (x)$, for the Cesàro–Riesz mean of any order $k>0$ of the number of representations of $n$ as a sum of two primes. Our approach is based on a double Mellin transform and the analytic continuation of certain functions arising therein.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11P32, 11N05

Retrieve articles in all journals with MSC (2010): 11P32, 11N05

Additional Information

Jörg Brüdern
Affiliation: Mathematisches Institut, Bunsenstrasse 3-5, 37073 Göttingen, Germany

Jerzy Kaczorowski
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland; and Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warsaw, Poland
MR Author ID: 96610

Alberto Perelli
Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
MR Author ID: 137910

Keywords: Goldbach problem, explicit formulae
Received by editor(s): January 22, 2018
Received by editor(s) in revised form: November 12, 2018
Published electronically: March 20, 2019
Additional Notes: This research was partially supported by a grant from Deutsche Forschungsgemeinschaft, by the grant PRIN-2015 “Number Theory and Arithmetic Geometry”, and by grant 2017/25/B/ST1/00208 “Analytic methods in number theory” from the National Science Centre, Poland. The third author is a member of the GNAMPA group of INdAM
Article copyright: © Copyright 2019 American Mathematical Society