PreprintCC BY 4.0arXiv
An explicit power-saving bound for Sárközy's Theorem on shifted primes, assuming GRH
Abstract
Assume the Generalised Riemann Hypothesis. If A⊆ {1,...,N} contains no two elements differing by p+1, p prime, then |A|≪ N89/90 + o(1).
Related
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- A Generalization of Sárközy's theorem in function fields
- The Furstenberg-Sárközy theorem for sums of an even number of odd powers
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- Shifted Symplectic Fibrations and Derived Thurston Theorem
BibTeX
@misc{gu2026explicit,
title = {{An explicit power-saving bound for Sárközy's Theorem on shifted primes, assuming GRH}},
author = {Qijun Gu and Minh Quang Nguyên},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14471},
eprint = {2609.14471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14471},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An explicit power-saving bound for Sárközy's Theorem on shifted primes, assuming GRH
AU - Qijun Gu
AU - Minh Quang Nguyên
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.14471
UR - https://arxiv.org/abs/2609.14471
AB - Assume the Generalised Riemann Hypothesis. If A⊆ {1,...,N} contains no two elements differing by p+1, p prime, then |A|≪ N^89/90 + o(1).
ER -