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
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
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Additional Information
- Jörg Brüdern
- Affiliation: Mathematisches Institut, Bunsenstrasse 3-5, 37073 Göttingen, Germany
- Email: bruedern@uni-math.gwdg.de
- 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: kjerzy@amu.edu.pl
- Alberto Perelli
- Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 137910
- Email: perelli@dima.unige.it
- 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: https://doi.org/10.1090/tran/7799
- MathSciNet review: 4024544