Related papers: Ratios of periods for tensor product motives

This is a survey of recent work on values of Rankin-Selberg $L$-functions of pairs of cohomological automorphic representations that are {\it critical} in Deligne's sense. The base field is assumed to be a CM field. Deligne's conjecture is…

In this paper, we give a description of Deligne's periods $c^\pm$ for tensor product of pure motives $M \otimes M'$ over $\mathbb{Q}$ in terms of the period invariants attached to $M$ and $M'$ by Yoshida. The period relations proved by the…

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…

In this paper, we study the special values of Rankin-Selberg L-functions as a continuation of [LLS24]. Utilizing the modular symbol approach, we prove the rationality and period relations for some critical values of Rankin-Selberg…

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times \mathrm{GL}(n-1)$. As a consequence, we prove the period relations for critical values of the Rankin-Selberg L-functions for…

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. As an…

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. In the…

We establish results on the rationality of ratios of successive critical values of Langlands-Shahidi $L$-functions, as they appear in the constant term of the Eisenstein series associated with the exceptional group of type $G_2$ over a…

Let $\mathcal K$ be an imaginary quadratic field. Let $\Pi$ and $\Pi'$ be irreducible generic cohomological automorphic representation of $GL(n)/{\mathcal K}$ and $GL(n-1)/{\mathcal K}$, respectively. Each of them can be given two natural…

Given a pure motive $M$ over $\mathbb{Q}$ with a multilinear algebraic structure $\mathsf{s}$ on $M$, and given a representation $V$ of the group respecting $\mathsf{s}$, we describe a functorial transfer $M^V$. We formulate a criterion…

We prove Deligne's conjecture for central critical values of certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$. The proof is base on rationality results for central critical values of triple product $L$-functions, which…

In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$-functions. We prove a formula expressing the critical values in the range of…

We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algebraic nature. We get a complete and conceptually clear answer…

We compute the second moment of a certain family of Rankin-Selberg $L$-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the…

In this paper we introduce an automorphic variant of the Deligne conjecture for tensor product of two motives over a quadratic imaginary field. On one hand, we define some motivic periods and rewrite the Deligne conjecture in terms of these…

This paper provides a proof of Deligne's conjecture for critical values of Hecke L-functions following a strategy originated by Harder and Schappacher.

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…

By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic…

In this paper, we derive a function field version of the Waldspurger formula for the central critical values of the Rankin-Selberg L-functions. This formula states that the central critical L-values in question can be expressed as the…

Michael HARRIS defined the arithmetic automorphic periods for certain cuspidal representations of $GL_{n}$ over quadratic imaginary fields in his Crelle paper 1997. He also showed that critical values of automorphic L-functions for…