Related papers: Central L-values and periods for GL(2)

We complement and offer a new perspective of the proof of a Motohashi-type formula relating the fourth moment of $L$-functions for $\mathrm{GL}_1$ with the third moment of $L$-functions for $\mathrm{GL}_2$ over number fields, studied…

We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet $L$-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula…

We establish explicit Ichino's formulae for the central values of the triple product $L$-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition 6.8 which generalizes a result…

We prove a cohomological formula for non-critical residues of degree eight automorphic $L$-functions of $\mathrm{GSp}(4) \times \mathrm{GL}(2)$ in the spirit of Beilinson conjecture. We rely on the cohomological interpretation of an…

The relative Langlands program introduced by Ben-Zvi--Sakellaridis--Venkatesh posits a duality structure exchanging automorphic periods and L-functions, which can be encoded by pairs of dual Hamiltonian actions. In work of the author and…

We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global…

We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were originally introduced and studied by Lewis and Zagier…

\begin{abstract} In this article, we will get non-trivial estimates for the central values of degree six Rankin-Selberg $L$-functions $L(1/2+it, \pi \times f)$ associated with a ${GL(3)}$ form $\pi$ and a ${GL(2)} $ form $f$ using the delta…

This paper is the first in a series of two dedicated to the study of period relations of the type $$ L(\frac{1}{2}+k,\Pi)\;\in\;(2\pi i)^{d\cdot k}\Omega_{(-1)^k}{\mathbb Q}(\Pi),\quad \frac{1}{2}+k\;\text{critical}, $$ for certain…

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…

We prove hybrid subconvexity bounds for a wide class of twisted L-functions $L(s,f\times \chi)$ at the central point, including a new instance of the Weyl subconvexity bound.

Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $\chi$ be a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa>12$. A subconvex bound for the…

Fix a Dirichlet character $\chi$ and a cuspidal GL$(2)$ eigenform $\phi$ with relatively prime conductors. Then we show that there are infinitely many cusp forms $\pi$ on GL$(3)$ such that $L(1/2, \pi \times \chi)$ and $L(1/2, \pi \times…

A representation of a specialization of a q-deformed class one lattice gl(\ell+1}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(P^{\ell}) of quasi-maps P^1 to P^{\ell} of degree d is proposed. For…

In this note, we derive a relative trace formula (RTF) using classical methods. We obtain a closed formula for the second moment of the central values of holomorphic cusp forms, a result originally established in Kuznetsov's preprint.

The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…

Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet $L$-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square…

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…

This article gives the Plancherel decomposition of $L^2\left(U(2)(F)\backslash SO_{2,3}(F)\right)$, where $F$ is a local field with characteristic $0$, and the relative character identities. Finally, we obtain a factorization of the global…

We prove a non-vanishing result for central values of $L$-functions on GL(3), by using the mollification method and the Kuznetsov trace formula.