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On a Smoothed Average of the Number of Goldbach Representations

In: Number Theory in Memory of Eduard Wirsing

Author

Listed:
  • Daniel A. Goldston

    (San Jose State University, Department of Mathematics and Statistics)

  • Ade Irma Suriajaya

    (Kyushu University, Faculty of Mathematics)

Abstract

Assuming the Generalized Riemann Hypothesis for the zeros of the Dirichlet L-functions with characters modulo q, we obtain a smoothed version of the average number of Goldbach representations for numbers which are multiples of a positive integer q. Such an average was first considered by Granville [11, 12] but without any smoothing factor. In this short article, we also show how the smoothing can be removed.

Suggested Citation

  • Daniel A. Goldston & Ade Irma Suriajaya, 2023. "On a Smoothed Average of the Number of Goldbach Representations," Springer Books, in: Helmut Maier & Jörn Steuding & Rasa Steuding (ed.), Number Theory in Memory of Eduard Wirsing, pages 145-156, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31617-3_10
    DOI: 10.1007/978-3-031-31617-3_10
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