Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 33 min ago
PreprintarXiv licencearXiv

A Log-Free n1/5 Bound for Chowla's Cosine Problem

  • Abhishek Shankar
Open at sourcePDFDOICite

Abstract

For a finite set S of positive integers, put K(S):=−minx∈𝕋∑s∈ Scos(2πsx). Bedert recently proved the uniform lower bound K(S)≥ |S|1/5−o(1). We remove the subpolynomial loss and prove that K(S)≥ c|S|1/5 for an absolute constant c>0. The proof combines two estimates from Bedert's argument with an exact averaging identity for the asymmetric boundaries of additive intersections. This identity replaces the multiplicative-amplification step responsible for the logarithmic loss.

Related

  1. A Half-Constant Upper Bound for Chowla's Cosine Problem
    Bryan Bu, Fayzan Khan, Hyunjun Yi +3
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Lower bounds for the magnitude of the minimum eigenvalue of graphs with applications to MaxCut and Chowla's cosine problem
    Fredy Yip
    arXivPreprintarXiv licenceFull textAnalysis & PDEsCombinatorics & discrete mathematicsarXiv
  3. An explicit lower bound for the unit distance problem
    Will Sawin
    arXiv (Cornell University)PreprintLicence not statedFull text30 citedCombinatorics & discrete mathematicsOpenAlex
  4. A Uniform Bound on Optimal Strategy Length in Water Transport Problem
    Tianyi Tao, Bohan Yang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. A near-quadratic lower bound for the Brown--Erdős--Sós (9,6)-problem
    Xiangliang Kong, Chong Shangguan, Xin Wang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{shankar2026logfree,
  title = {{A Log-Free $n^1/5$ Bound for Chowla's Cosine Problem}},
  author = {Abhishek Shankar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05338},
  eprint = {2609.05338},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05338},
}
RIS
TY  - UNPB
TI  - A Log-Free n^1/5 Bound for Chowla's Cosine Problem
AU  - Abhishek Shankar
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05338
UR  - https://arxiv.org/abs/2609.05338
AB  - For a finite set S of positive integers, put K(S):=−min_x∈𝕋∑_s∈ Scos(2πsx). Bedert recently proved the uniform lower bound K(S)≥ |S|^1/5−o(1). We remove the subpolynomial loss and prove that K(S)≥ c|S|^1/5 for an absolute constant c>0. The proof combines two estimates from Bedert's argument with an exact averaging identity for the asymmetric boundaries of additive intersections. This identity replaces the multiplicative-amplification step responsible for the logarithmic loss.
ER  -