Related papers: Ichino period for CM forms

Waldspurger's formula gives an identity between the norm of a torus period and an L-function of the twist of an automorphic representation on GL(2). For any two Hecke characters of a fixed quadratic extension, one can consider the two torus…

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…

Lapid and Mao conjectured Ichino-Ikeda type formula of Whittaker periods for any quasi-split reductive groups and metaplectic groups. In this paper, we prove this formula for any irreducible cuspidal globally generic automorphic…

The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the…

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…

We reprove a Waldspurger's formula which relates the toric periods and the central values of L-functions of GL2. Our technique, different from the original theta-correspondence approach and the more recent relative trace formula, relies on…

In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one…

We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological techniques for working with periods introduced in [Mol21],…

In our previous work, he second and the third named authors constructed the Ikeda type lift for the exceptional group $E_{7,3}$ from an elliptic modular cusp form. In this paper, we prove an explicit formula for the period or the Petersson…

The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. This work introduces the mathematical machinery to derive the complete moduli dependence of…

We formulate a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for $\mathrm{GL}(2)$. We introduce a…

In this paper, we extend the work of Humphries and Khan [HK20] to establish an explicit version of Watson--Ichino formula for $L(1/2,f\otimes\mathrm{ad} g)$, where $f$ is a Hecke--Maass form and $g$ is a CM newform.

We study "quadratic periods" on quaternionic Shimura varieties and formulate an integral refinement of Shimura's conjecture regarding Petersson inner products of automorphic forms that are related by the Jacquet-Langlands correspondence.…

In this paper, we give Thomae type formula for \KK surfaces $\cS$ given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type…

We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of such transforms is shown to arise naturally from the expectation that the Schwartz space on the real line,…

We show how to evaluate the periods in Seiberg-Witten theories and in K3-fibered Calabi-Yau manifolds by using fibrations of the theories. In the Seiberg-Witten theories, it is shown that the dual pair of fields can be constructed from the…

Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida regarding the {\it congruence number}…

In this paper we extend the calculation of the geometric Waldspurger periods from our paper math/0510110 to the case of ramified coverings. We give some applications to the study of Whittaker coefficients of the theta-lifting of automorphic…

We show that the Grothendieck period conjecture holds for the Kummer surface associated with the square of a CM elliptic curve. This means that the period isomorphism is dense in the torsor of motivic periods. In other words, the…

In the theory of complex multiplication, it is important to construct class fields over CM fields. In this paper, we consider explicit $K3$ surfaces parametrized by Klein's icosahedral invariants. Via the periods and the Shioda-Inose…