Iwasawa invariants of modular forms with a_p=0

2023/02/11 by Rylan Gajek-Leonard, Gajek-Leonard, Rylan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2302.05748

Abstract

Fix a prime p and a cuspidal newform f of level coprime to p with a_p=0. Attached to f are signed p-adic L-functions L_p^±(f) and Mazur-Tate elements θ_n(f), both of which encode arithmetic data about f along the cyclotomic Z_p-extension of Q. We compute the Iwasawa invariants of Mazur-Tate elements in terms of the corresponding invariants of the signed p-adic L-functions. As corollaries, we determine the p-adic valuation of critical values of the L-function of f, and describe a relation between the Iwasawa invariants of congruent modular forms of weights 2 and p+1. Our results provide an asymptotic method for computing the signed Iwasawa invariants attached to newforms of any weight k≥ 2 with a_p=0.

Cited by

• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

Related

• Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
• Congruences of p-adic L-functions of modular forms at non-ordinary primes
• On the Iwasawa invariants of Kato's zeta elements for modular forms
• On Iwasawa invariants of modular forms with reducible and non-p-distinguished residual Galois representations
• On pairs of p-adic analogues of the conjectures of Birch and Swinnerton-Dyer