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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Explicit formulae for averages of Goldbach representations
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by Jörg Brüdern, Jerzy Kaczorowski and Alberto Perelli PDF
Trans. Amer. Math. Soc. 372 (2019), 6981-6999 Request permission


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.
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Additional Information
  • Jörg Brüdern
  • Affiliation: Mathematisches Institut, Bunsenstrasse 3-5, 37073 Göttingen, Germany
  • Email:
  • 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
  • Email:
  • Alberto Perelli
  • Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
  • MR Author ID: 137910
  • Email:
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 6981-6999
  • MSC (2010): Primary 11P32, 11N05
  • DOI:
  • MathSciNet review: 4024544