Related papers: Algebraicity of critical values of adjoint $L$-fun…

We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on ${\rm GSp}_4$ whose archimedean components belong to either discrete series representations or spherical principal series representations.…

Let $\mathit{\Pi}$ be a cohomological irreducible cuspidal automorphic representation of ${\rm GL}_2(\mathbb{A}_{\mathbb F})$ with central character $\omega_{\mathit{\Pi}}$ over a totally real number field ${\mathbb F}$. In this paper, we…

For a globally generic cuspidal automorphic representation $\mathit{\Pi}$ of a quasi-split reductive group $G$ over $\mathbb Q$, E. Lapid and Z. Mao proposed a conjecture on the decomposition of the global Whittaker functionals on…

In this paper, we prove Deligne's conjecture on the algebraicity of critical values of symmetric power $L$-functions associated to modular forms of weight greater than four. We also prove new cases of Blasius' conjecture on the algebraicity…

We prove algebraicity results for critical $L$-values attached to the group $\text{GSp}_4 \times \text{GL}_2$, and for Gan--Gross--Prasad periods which are conjecturally related to central $L$-values for $\text{GSp}_4 \times \text{GL}_2…

In this paper, we prove Deligne's conjecture for symmetric sixth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on a different approach. We define automorphic periods associated to globally generic…

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…

We prove the expected algebraicity property for the critical values of character twists of the standard $L$-function associated to vector-valued holomorphic Siegel cusp forms of archimedean type $(k_1, k_2, \ldots, k_n)$, where $k_n \geq…

In this survey, we review the known results on the algebraicity of critical values of Hecke $L$-functions and explain the new developments in \cite{Kings-Sprang}.

We show entireness of complete adjoint L-functions associated to \textbf{any} cuspidal representations of $\GL(3)$ or $\GL(4)$ over an arbitrary global field. Twisted cases are also investigated.

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 explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of…

In a previous article we had proved an algebraicity result for the central critical value for L-functions for GL(n) x GL(n-1) over Q assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this…

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,…

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…

The goal of this paper is to provide a refinement of a formula proved by the first author which expresses some critical values of automorphic $L$-functions on unitary groups as Petersson norms of automorphic forms. Here we provide a Galois…

We construct $p$-adic $L$-functions interpolating the critical values of the degree eight $L$-functions of ${\rm GSp}(4)\times {\rm GL}(2)$ for cuspidal automorphic representations generated by $p$-ordinary Siegel modular forms of genus two…

In this paper we prove rationality results of critical values for $L$-functions attached to representations in the residual spectrum of $\mathrm{GL}_4(\mathbb{A})$. We use the Jacquet-Langlands correspondence to describe their partial…

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…

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…