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ON AN AVERAGE GOLDBACH REPRESENTATION FORMULA OF FUJII

Part of: Zeta and $L$-functions: analytic theory Additive number theory; partitions Multiplicative number theory

Published online by Cambridge University Press:  17 January 2023

DANIEL A. GOLDSTON Open the ORCID record for DANIEL A. GOLDSTON [Opens in a new window]  and
ADE IRMA SURIAJAYA Open the ORCID record for ADE IRMA SURIAJAYA [Opens in a new window]
DANIEL A. GOLDSTON
Affiliation:
Department of Mathematics and Statistics San Jose State University San Jose, California USA daniel.goldston@sjsu.edu
ADE IRMA SURIAJAYA*
Affiliation:
Faculty of Mathematics Kyushu University Fukuoka Japan
*
adeirmasuriajaya@math.kyushu-u.ac.jp
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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.

MSC classification

Primary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11N05: Distribution of primes 11N37: Asymptotic results on arithmetic functions 11P32: Goldbach-type theorems; other additive questions involving primes

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Type
Article
Information
Nagoya Mathematical Journal , Volume 250 , June 2023 , pp. 511 - 532
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

Suriajaya was supported by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant Numbers 18K13400 and 22K13895, and also by the Ministry of Education, Culture, Sports, Science and Technology Initiative for Realizing Diversity in the Research Environment.

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