# The error term in the Ces\\\`{a}ro mean of the prime pair singular series

Source: [The error term in the Ces\\\`{a}ro mean of the prime pair singular series](<https://www.sota2.com/research/paper/68fa58901e209131ce9af703>)

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

Data updated: 2025-10-25T15:24:38.666Z

Authors: D. A. Goldston, Ade Irma Suriajaya

Published: 2020-07-29T05:58:05.000Z

## Abstract

We show that the error term in the asymptotic formula for the Ces{\\\`a}ro mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures cannot be too small and oscillates.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2007.14616>)

[PDF](<https://arxiv.org/pdf/2007.14616.pdf>)