Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields

DOI10.1515/CRELLE.2011.018zbMath1288.11049arXiv0903.1625MaRDI QIDQ3002713

Fabian Januszewski

Publication date: 24 May 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.1625

zbMATH Keywords

\(p\)-adic \(L\)-functionmodular symbolRankin-Selberg \(L\)-function

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Arithmetic aspects of modular and Shimura varieties (11G18) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (9)

\(p\)-adic \(L\)-functions for Rankin-Selberg convolutions over number fields ⋮ On Shalika models and \(p\)-adic \(L\)-functions ⋮ Bianchi modular symbols and \(p\)-adic \(L\)-functions ⋮ On period relations for automorphic 𝐿-functions I ⋮ Test vectors for Rankin-Selberg \(L\)-functions ⋮ The nonvanishing hypothesis at infinity for Rankin-Selberg convolutions ⋮ Overconvergent cohomology, \(p\)-adic \(L\)-functions and families for \(\mathrm{GL}(2)\) over CM fields ⋮ Spherical varieties and norm relations in Iwasawa theory ⋮ P-Adic Integration on Ray Class Groups and Non-ordinary p-Adic L-Functions

Uses Software

• SageMath

Cites Work

• Relative modular symbols and \(p\)-adic Rankin-Selberg convolutions
• Arithmetic subgroups of algebraic groups
• On \(L\)-functions of elliptic curves and cyclotomic towers
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• Conducteur des représentations du groupe linéaire
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• On the periods of modular forms
• The special values of the zeta functions associated with Hilbert modular forms
• Automorphic forms on \(GL(3)\). I, II
• \(p\)-adic \(L\)-functions for \(\text{GL}(2n)\)
• On the zeta functions of Shimura varieties and periods of Hilbert modular forms
• Converse theorems for \(\text{GL}_n\)
• Arithmetic of Weil curves
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Groupes reductifs
• On the \(\zeta\)-functions of a division algebra
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• Arithmetic of algebraic tori
• Self-adjoint groups
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Rankin-Selberg Convolutions
• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II
• The special values of the zeta functions associated with cusp forms
• NON-ARCHIMEDEAN INTEGRATION AND JACQUET-LANGLANDSp-ADICL-FUNCTIONS
• On an explicit formula for class-$1$ “Whittaker functions” on $GL_n $ over $\beta $-adic fields
• Special Values of Triple Product L-Functions
• Period relations and \(p\)-adic measures

This page was built for publication: Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields