A mean value of the representation function for the sum of two primes in arithmetic progressions

Yuta Suzuki

Type: Article

Publication Date: 2016-10-04

Citations: 8

DOI: https://doi.org/10.1142/s1793042117500518

Abstract

In this paper, assuming a variant of the Generalized Riemann Hypothesis, which does not exclude the existence of real zeros, we prove an asymptotic formula for the mean value of the representation function for the sum of two primes in arithmetic progressions. This is an improvement of the result of F. Rüppel in 2009, and a generalization of the result of A. Languasco and A. Zaccagnini concerning the ordinary Goldbach problem in 2012.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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Works That Cite This (9)

Action	Title	Year	Authors
+	Asymptotics of Goldbach Representations.	2018	Gautami Bhowmik Karin Halupczok
+	On a smoothed average of the number of Goldbach representations	2023	D. A. Goldston Ade Irma Suriajaya
+	On a Smoothed Average of the Number of Goldbach Representations	2023	D. A. Goldston Ade Irma Suriajaya
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+	A survey on the theory of multiple Dirichlet series with arithmetical coefficients on the numerators	2021	Kohji Matsumoto
+ PDF Chat	Cesàro averages for Goldbach representations with summands in arithmetic progressions	2021	Marco Cantarini Alessandro Gambini Alessandro Zaccagnini
+	A Montgomery–Hooley theorem for the number of Goldbach representations	2022	Claus Bauer
+ PDF Chat	GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET <i>L</i> ‐FUNCTIONS	2018	Gautami Bhowmik Karin Halupczok Kohji Matsumoto Yuta Suzuki
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Works Cited by This (8)

Action	Title	Year	Authors
+ PDF Chat	Sums of many primes	2012	Alessandro Languasco Alessandro Zaccagnini
+	CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES	2007	Shigeki Egami Kohji Matsumoto
+ PDF Chat	The number of Goldbach representations of an integer	2011	Alessandro Languasco Alessandro Zaccagnini
+ PDF Chat	On Linnik's theorem on Goldbach numbers in short intervals and related problems	1994	Alessandro Languasco Alberto Perelli
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan
+ PDF Chat	Mean representation number of integers as the sum of primes	2010	Gautami Bhowmik Jan‐Christoph Schlage‐Puchta
+ PDF Chat	An additive problem of prime numbers, II	1991	Akio Fujii
+ PDF Chat	An additive problem of prime numbers	1991	Akio Fujii