Related papers: A generalized Rubin formula for Hecke characters

In a recent paper, Castella and Hsieh proved results for Selmer groups associated with Galois representations attached to newforms twisted by Hecke characters of an imaginary quadratic field. These results are obtained under the so-called…

In this paper, we generalize a work of Rohrlich. Let $K/\mathbb{Q}$ be an imaginary quadratic field and $\phi$ be a Hecke character of $K$ of infinite type (1,0) whose restriction to $\mathbb{Q}$ is the quadratic character corresponding to…

We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection…

We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical…

We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…

We first introduce a new presentation for the mirabolic Hecke algebra $\mathscr{H}_{n,R}(q)$ over an arbitrary commutative ring $R$ and derive a new basis. Based on this presentation, specializing to the case of $\mathscr{H}_n(q)$ over the…

We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also…

Let K/F be a quadratic extension of number fields. After developing a theory of the Eisenstein series over F, we prove a formula which expresses a partial zeta function of K as a certain integral of the Eisenstein series. As an application,…

We generalize our previous method on subconvexity problem for $\mathrm{GL}_2 \times \mathrm{GL}_1$ with cuspidal representations to Eisenstein series, and deduce a Burgess-like subconvex bound for Hecke characters, i.e., the bound…

Let $F/K$ be an abelian extension of number fields with $F$ either CM or totally real and $K$ totally real. If $F$ is CM and the Brumer-Stark conjecture holds for $F/K$, we construct a family of $G(F/K)$--equivariant Hecke characters for…

Assuming the Riemann hypothesis for $L$-functions attached to primitive Dirichlet characters, modular cusp forms, and their tensor products and symmetric squares, we write down explicit finite sets of Hecke operators that span the Hecke…

We prove the transfer congruence between $p$-adic Hecke $L$-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer's congruence. The ingredients of the proof include the comparison between…

As a continuation of previous work, we establish sum expressions for $p$-adic Hecke $L$-functions of totally real fields in the sense of Delbourgo, assuming a totally real analog of Heegner hypothesis. This is done by finding explicit…

In this article, we present a generalized Hecke's integral formula for an arbitrary extension $E/F$ of number fields. As an application, we present relative versions of the residue formula and Kronecker's limit formula for the "relative"…

We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's…

Let $K=\mathbb{Q}(\sqrt{-D})$ be an imaginary number field, $(p)=\mathfrak{p}\mathfrak{p}'$ be a split odd prime and $\psi$ be a Hecke character of conductor $\mathfrak{p}$. Let $L(s,\psi)$ be the associated $L$-function. We prove the…

We generalize classical Hobson's formula concerning partial derivatives of radial functions on a Euclidean space to a formula in the Dunkl analysis. As applications we give new simple proofs of known results involving Maxwell's…

We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced $L$-parameters of $p$-adic reductive groups and apply it to the study of the Howe correspondence.

In this paper we prove a version of Deligne's conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of…

Recently Delorme and Opdam have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series…