Iwasawa Theory of Elliptic Curves in Quadratic Twist Families

2025/07/28 by Kundu, Debanjana, Müller, Katharina
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.21339

Abstract

In this article, we use two different approaches -- one algebraic and the other analytic -- to study the variation of Iwasawa invariants of rational elliptic curves in some quadratic twist families. The analytic approach involves a thorough investigation of half-integral weight modular forms. On the other hand, the algebraic proof requires studying the BDP-Selmer groups and the fine Selmer groups.

Citations

• The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture
• λ-invariant stability in families of modular Galois representations
• Asymptotic formula for Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic extensions
• Binary quartic forms having bounded invariants, and the boundedness of\n the average rank of elliptic curves
• Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

Related

• Iwasawa theory and ranks of elliptic curves in quadratic twist families
• Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes
• Iwasawa theory for elliptic curves
• Congruent elliptic curves over some p-adic Lie extensions
• Iwasawa Theory for Elliptic Curves at Unstable Primes