On an Average Goldbach Representation Formula of Fujii

Abstract

Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditional version of this result, and obtain applications conditional on various conjectures on zeros of the Riemann zeta-function.

22 pages, to appear in Nagoya Math. J

References in corpus (1)

• The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function

Cited by in corpus (4)

• The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function
• The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function
• On a smoothed average of the number of Goldbach representations
• The average number of Goldbach representations over multiples of $q$