Canonical periods and congruence formulae

1999/06/01 by V. Vatsal, Vinayak Vatsal · 7 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · doi:10.1215/s0012-7094-99-09811-3

Abstract

The purpose of this article is to show how congruences between the Fourier coefficients of Hecke eigenforms give rise to corresponding congruences between the algebraic parts of the critical values of the associated L-functions. This study was initiated by B. Mazur in his fundamental work on the Eisenstein ideal (see [Maz77] and [Maz79]) where it was made clear that congruences for analytic L-values were closely related to

Citations

• On ordinary ?-adic representations associated to modular forms
• Modular Elliptic Curves and Fermat's Last Theorem

Cited by

• Stable free lattices in residually reducible Galois deformations and control theorem of Selmer groups
• Eisenstein cohomology and congruences for the ratios of Rankin--Selberg L-functions
• Congruences for the ratios of Rankin--Selberg L-functions
• Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular form
• 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
• Heegner points at Eisenstein primes and twists of elliptic curves

Related

• Congruences between Hilbert modular forms of weight 2, and special values of their L-functions
• Congruence conditions for the mod λ values of the Fourier coefficients of classical eigenforms
• GL₂\timesGSp₂ L-values and Hecke eigenvalue congruences
• Periods of Jacobi forms and Hecke operator
• A note on Fourier coefficients of Hecke eigenforms in short intervals