On triple product L-functions and a conjecture of Harris–Venkatesh
E Lecouturier - International Mathematics Research Notices, 2023 - academic.oup.com
Harris and Venkatesh made a conjecture relating the derived Hecke operators and the
adjoint motivic cohomology in the setting of weight one modular forms. This conjecture was …
adjoint motivic cohomology in the setting of weight one modular forms. This conjecture was …
Critical Lambda-adic modular forms and bi-ordinary complexes
F Castella, C Wang-Erickson - arXiv preprint arXiv:2406.08460, 2024 - arxiv.org
We produce a flat $\Lambda $-module of $\Lambda $-adic critical slope overconvergent
modular forms, producing a Hida-type theory that interpolates such forms over $ p $-adically …
modular forms, producing a Hida-type theory that interpolates such forms over $ p $-adically …
The Harris-Venkatesh conjecture for derived Hecke operators II: a unified Stark conjecture
R Zhang - arXiv preprint arXiv:2305.08956, 2023 - arxiv.org
We formulate a unified conjecture for weight-$1 $ modular forms that combines the Stark
conjecture and the Harris-Venkatesh conjecture, suggesting that the leading coefficient of …
conjecture and the Harris-Venkatesh conjecture, suggesting that the leading coefficient of …
Motivic action for Siegel modular forms
A Horawa, K Prasanna - arXiv preprint arXiv:2307.04115, 2023 - arxiv.org
We study the coherent cohomology of automorphic sheaves corresponding to Siegel
modular forms $ f $ of low weight on ${\rm GSp}(4) $ Shimura varieties. Inspired by the work …
modular forms $ f $ of low weight on ${\rm GSp}(4) $ Shimura varieties. Inspired by the work …
Modular Gelfand pairs and multiplicity-free representations
R Zhang - International Mathematics Research Notices, 2024 - academic.oup.com
Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-
freeness theorem for finitely-generated modules with commutative endomorphism rings …
freeness theorem for finitely-generated modules with commutative endomorphism rings …
The Harris-Venkatesh conjecture for derived Hecke operators III: local constants
R Zhang - arXiv preprint arXiv:2301.00612, 2023 - arxiv.org
The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement
with the Stark conjecture for imaginary dihedral modular forms of weight $1 $. In this paper …
with the Stark conjecture for imaginary dihedral modular forms of weight $1 $. In this paper …