Related papers: New integral representations for Rankin-Selberg L-…

While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in…

We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation between these p-adic L-functions and families of Galois…

Given three irreducible, admissible, infinite dimensional complex representations of GL2(F), with F a local field, the space of trilinear functionals invariant by the group has dimension at most one. When it is one we provide an explicit…

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.

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $\text{GL}(n)\times \text{GL}(n)$ and $\text{GL}(n)\times \text{GL}(n-1)$, for all generic cohomological representations. As a consequence, we prove…

We prove that the coefficients of a $\mathrm{GL}_3\times \mathrm{GL}_2$ Rankin--Selberg $L$-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result \cite{FKM1}…

We use the uniqueness of various invariant functionals on irreducible unitary representations of PGL(2,R) in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new…

We consider $L$-functions attached to representations of the Galois group of the function field of a curve over a finite field. Under mild tameness hypotheses, we prove non-vanishing results for twists of these $L$-functions by characters…

We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system $E$ of…

In the paper we prove an explicit formula for the central values of certain Rankin L-functions. These L-functions are L-functions of Hilbert newforms over a totally real field F, twisted by unitary Hecke characters of a totally imaginary…

We formulate for function fields an analog of Serre's conjecture on the modularity of 2-dimensional irreducible mod l representations of the absolute Galois group of Q: our analog is not restricted to 2-dimensional represntations. While the…

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 2023, Li, Du, Yi proved a uniqueness theorem for L functions in the extended Selberg class under the assumptions of positive degree, a shared functional equation, and the sharing of three complex values. This was later strengthened by…

The thesis gave a fine study on the distribution of the coefficients of automorphic L-functions for GL(m) with m>1. In particular we have treated two types of problems: change of signs of these coefficients (when they are real) and their…

We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity…

Recently we propose a class of infinite-dimensional integral representations of classical gl(n+1)-Whittaker functions and local Archimedean local L-factors using two-dimensional topological field theory framework. The local Archimedean…

Let $\pi_1,\pi_2$ be a pair of cuspidal complex, or $\ell$-adic, representations of the general linear group of rank $n$ over a non-archimedean local field $F$ of residual characteristic $p$, different to $\ell$. Whenever the local…

The author reviews results and conjectures of Selberg on a class of Dirichlet series functions which share properties with the Riemann zeta function, and he relates this work to the theory of Artin L-functions.

Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ defined on $GL_n(\mathbb{A}_E)$ and $GL_m(\mathbb{A}_F)$, respectively, with $E$ and $F$ solvable algebraic number fields we deduce a prime number theorem for the…

In this article, we will prove subconvex bounds for $GL(3) \times GL(2)$ $L$-functions in the depth aspect.