Rank stability of elliptic curves in certain non-abelian extensions

IF 0.8 3区数学 Q2 MATHEMATICS Mathematische Nachrichten Pub Date : 2025-01-08 DOI:10.1002/mana.202400357

Siddhi Pathak, Anwesh Ray

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引用次数: 0

Abstract

Let $E_{/ Q}$ be an elliptic curve with rank $E (Q) = 0$ . Fix an odd prime $p$ , a positive integer $n$ , and a finite abelian extension $K / Q$ with rank $E (K) = 0$ . In this paper, we show that there exist infinitely many extensions $L / K$ such that $L / Q$ is Galois with $Gal (L / Q) ≃ Gal (K / Q) ⋉ Z / p^{n} Z$ , and rank $E (L) = 0$ . This is an extension of earlier results on rank stability of elliptic curves in cyclic extensions of prime power order to a non-abelian setting. We also obtain an asymptotic lower bound for the number of such extensions, ordered by their absolute discriminant.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index

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Issue Information Contents Issue Information Contents Rank stability of elliptic curves in certain non-abelian extensions