相关论文: The special values of the standard $L$-functions f…

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

We prove an algebraicity result for the central critical value of certain Rankin-Selberg L-functions for GL(n) x GL(n-1). This is a generalization and refinement of some results of Harder, Kazhdan-Mazur-Schmidt, Mahnkopf, and…

We prove algebraicity of critical values of certain Spin $L$-functions. More precisely, our results concern $L(s, \pi \otimes \chi, Spin)$ for cuspidal automorphic representations $\pi$ associated to a holomorphic Siegel eigenform on…

Let $\pi$ be a cuspidal automorphic representation of $\operatorname{GL}_2$ over a totally real number field $F$. Let $K$ be a totally imaginary quadratic extension of $F$. We estimate central values of the $\operatorname{GL}_2 \times…

We provide an explicit integral representation for L-functions of pairs (F,g) where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic newform, both of squarefree levels and of equal weights. When F,g have level one,…

We prove an integrality result for the value at s=1 of the adjoint L-function associated to a cohomological cuspidal automorphic representation on GL(n) over any number field. We then show that primes (outside an exceptional set) dividing…

We explicitly compute the special values of the standard $L$-function $L(s, F_{12}, \mathrm{St})$ at the critical points $s\in\{-8, -6, -4, -2, 0, 1, 3, 5, 7, 9\}$, where $F_{12}$ is the unique (up to a scalar) Siegel cusp form of degree…

Fix $n \geq 2$ an integer, and let $F$ be a totally real number field. We derive estimates for the finite parts of the $L$-functions of irreducible cuspidal $\operatorname{GL}_n({\bf{A}}_F)$-automorphic representations twisted by class…

We prove an algebraicity result for certain critical value of adjoint $L$-functions for ${\rm GSp}_4$ over a totally real number field in terms of the Petersson norm of normalized generic cuspidal newforms on ${\rm GSp}_4$. This is a…

The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\Pi$ of $\mathrm{GL}(2n)$ over a totally real field $F$ admitting a Shalika model. We use a modular…

The standard twist $F(s,\alpha)$ of $L$-functions $F(s)$ in the Selberg class has several interesting properties and plays a central role in the Selberg class theory. It is therefore natural to study its finer analytic properties, for…

We study the algebraicity of the central critical values of twisted triple product $L$-functions associated to motivic Hilbert cusp forms over a totally real \'etale cubic algebra in the totally unbalanced case. The algebraicity is…

The purpose of this semi-expository article is to give another proof of a classical theorem of Shimura on the critical values of the standard L-function attached to a Hilbert modular form. Our proof is along the lines of previous work of…

We prove several results on the distribution of values of $L$-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power…

Let $p$ be an odd prime, $N$ a square-free odd positive integer prime to $p$, $\pi$ a $p$-ordinary cohomological irreducible cuspidal automorphic representation of $\mathrm{GSp}_4(\mathbb{A}_\mathbb{Q})$ of principal level $N$ and Iwahori…

Additive twists are important invariants associated to holomorphic cusp forms; they encode the Eichler--Shimura isomorphism and contain information about automorphic $L$-functions. In this paper we prove that central values of additive…

Let $\pi$ be an irreducible cuspidal automorphic generic representation of $\mathrm{Sp}_{2n}(\mathbb{A})$ and let $\chi:F^\times\backslash \mathbb{A}^\times\to \mathbb{C}^\times$ be a unitary idele class character. In this note, we present…

We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we…

Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for $GL_3(\mathbb R)$, we obtain the first moment of central values of $L(s,f\otimes \phi)$, where…