Modular forms in characteristic $\ell$ and special values of their $L$-functions

DOI10.1215/S0012-7094-86-05346-9zbMath0618.10026OpenAlexW1534024036MaRDI QIDQ1089033

Publication date: 1986

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.dmj/1077305204

zbMATH Keywords

congruences group cohomology modular forms modular symbols Hecke eigenvalues special values of L-functions

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Cohomology of arithmetic groups (11F75)

Related Items (62)

On torsion in the cohomology of $\operatorname{PSL}_2 (\mathbb Z[1/N)$] ⋮ On torsion in the cohomology of certain $S$-arithmetic groups ⋮ Lifting modular mod $l$ representations ⋮ Computational Arithmetic of Modular Forms ⋮ $p$-adic $L$-functions and $p$-adic periods of modular forms ⋮ The -adic -functions of evil Eisenstein series ⋮ General Serre weight conjectures ⋮ Slopes of modular forms and reducible Galois representations, an oversight in the ghost conjecture ⋮ Galois representations attached to tensor products of arithmetic cohomology ⋮ A NOTE ON CONTROL THEOREMS FOR QUATERNIONIC HIDA FAMILIES OF MODULAR FORMS ⋮ $p$-adic $L$-functions and the geometry of Hida families ⋮ Congruences between cusp forms: The $(p,p)$ case ⋮ On the reductions of certain two-dimensional crystabelline representations ⋮ A $p$-adic analytic family of the $D$-th Shintani lifting for a Coleman family and congruences between the central $L$-values ⋮ On Serre's conjecture for mod $\ell $ Galois representations over totally real fields ⋮ A numerical approach toward the $p$-adic Beilinson conjecture for elliptic curves over $\mathbb{Q}$ ⋮ Toric Periods and 𝑝-adic Families of Modular Forms of Half-Integral Weight ⋮ Zeta morphisms for rank two universal deformations ⋮ Reduction mod $p$ of cuspidal representations of $\text{GL}_2(\mathbb F_{p^n})$ and symmetric powers. ⋮ On mod $p$ nonvanishing of special values of $L$-functions associated with cusp forms on $\mathrm{GL}_{2}$ over imaginary quadratic fields ⋮ Mazur-Tate elements of nonordinary modular forms ⋮ $p$-adic Asai $L$-functions of Bianchi modular forms ⋮ Mod 2 and mod 5 icosahedral representations ⋮ Darmon cycles and the Kohnen-Shintani lifting ⋮ A reciprocity map and the two-variable $p$-adic $L$-function ⋮ Critical $p$-adic $L$-functions ⋮ Bianchi modular symbols and $p$-adic $L$-functions ⋮ Computing the number of certain Galois representations mod $p$ ⋮ Congruences with Eisenstein series and -invariants ⋮ The Steinberg symbol and special values of $L$-functions ⋮ Modular representations of $\text{GL}(3,\mathbb{F}_p)$, symmetric squares, and mod-$p$ cohomology of $\text{GL}(3,\mathbb{Z})$ ⋮ Canonical periods and congruence formulae ⋮ On the trace formula for Hecke operators on congruence subgroups ⋮ A remark on non-integral $p$-adic slopes for modular forms ⋮ The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication ⋮ On the weights of mod $p$ Hilbert modular forms ⋮ Automorphic lifts of prescribed types ⋮ On the faithfulness of parabolic cohomology as a Hecke module over a finite field ⋮ On the computation of coefficients of modular forms: The reduction modulo $p$ approach ⋮ $p$-adic family of half-integral weight modular forms via overconvergent Shintani lifting ⋮ Unnamed Item ⋮ Serre weights and the Breuil-Mézard conjecture for modular forms ⋮ Remarks on Kato's Euler systems for elliptic curves with additive reduction ⋮ Explicit computations of Hida families via overconvergent modular symbols ⋮ Euler systems for Rankin-Selberg convolutions of modular forms ⋮ Integral periods for modular forms ⋮ Arithmetic of elliptic curves and diophantine equations ⋮ Torsion classes in cohomology and Galois representations ⋮ Exceptional zeros and $\mathcal {L}$-invariants of Bianchi modular forms ⋮ Slopes of modular forms and the ghost conjecture, II ⋮ Congruences between Siegel modular forms on the level of group cohomology ⋮ Weight reduction for mod $\ell $ Bianchi modular forms ⋮ On the reductions of certain two-dimensional crystalline representations ⋮ Interpolation of Beilinson-Kato elements and $p$-adic $L$-functions ⋮ $p$-adic families of $\mathfrak{d}$th Shintani liftings ⋮ Overconvergent Modular Symbols ⋮ Upper bounds for constant slope $p$-adic families of modular forms ⋮ Indivisibility of central values of $L$-functions for modular forms ⋮ An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the $\operatorname{mod} p$ cohomology of $\text{GL}(n,\mathbb{Z})$ ⋮ Galois representations with conjectural connections to arithmetic cohomology ⋮ Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients ⋮ Modular representations of $\text{PGL}_ 2$ and automorphic forms for Shimura curves

Cites Work

This page was built for publication: Modular forms in characteristic $\ell$ and special values of their $L$-functions

Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions