# On an Average Goldbach Representation Formula of Fujii

Source: [On an Average Goldbach Representation Formula of Fujii](<https://www.sota2.com/research/paper/68fa5a7e1e209131ce9c04a3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:05.202Z

Authors: D. A. Goldston, Ade Irma Suriajaya

Published: 2021-10-27T08:11:21.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2110.14250>)

[PDF](<https://arxiv.org/pdf/2110.14250.pdf>)