On a conjecture of Rudin on squares in arithmetic progressions

DOI10.1112/S1461157013000259zbMath1314.11059arXiv1301.5122WikidataQ123365452 ScholiaQ123365452MaRDI QIDQ5170250

Xavier Xarles, Enrique González-Jiménez

Publication date: 23 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.5122

zbMATH Keywords

projective curvearithmetic progressionSelmer groupnumber of squares

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Counting solutions of Diophantine equations (11D45) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Primes in congruence classes (11N13) Arithmetic progressions (11B25)

Related Items (4)

Four rational squares in arithmetic progressions and a family of elliptic curves with positive Mordell-Weil rank ⋮ Powers in arithmetic progressions ⋮ Diagonal genus 5 curves, elliptic curves over $\mathbb {Q}(t)$, and rational diophantine quintuples ⋮ On arithmetic progressions on Edwards curves

Uses Software

• Magma
• OEIS
• ecdata

Cites Work

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• On Heterogeneous Spaces
• Signes locaux des courbes elliptiques en 2 et 3
• Squares in arithmetical progressions I.
• Independence of rational points on twists of a given curve
• Uniformity of rational points

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