Related papers: Functoriality and special values of L-functions

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.

We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in…

Let $\pi$ be a cuspidal automorphic representation for $\mathrm{GL}(n)$ over a number field. We establish a conditional upper bound on the number of cuspidal isobaric summands in the symmetric $k$-th power lift of $\pi$, assuming that the…

Based on the full similarity in algebraic properties and differentiation rules between quaternionic (H-) holomorphic and complex (C-) holomorphic functions, we assume that there exists one holistic notion of a holomorphic function that has…

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied…

We derive a family of approximations for L-functions of Hecke cusp eigenforms, according to a recipe first described by Matiyasevich for the Riemann xi function. We show that these approximations converge to the true L-function and point…

We prove Deligne's conjecture for symmetric fifth $L$-functions of elliptic newforms of weight greater than $5$. As a consequence, we establish period relations between motivic periods associated to an elliptic newform and the…

In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic cusp forms. The foundations of this construction are based in the…

We use the triality automorphism of simple algebraic groups of type $D_4$ to prove some new instances of global Langlands functorial lifting. In particular, we prove the (weak) spin lifting from ${\rm GSp}_6$ to ${\rm GL}_8$ and the tensor…

The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…

We introduce an L-series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these L-series and, as an application, we formulate and prove a summation formula for the holomorphic…

We come back to the construction of p-adic L-functions attached to cusp forms of even weight k in the spirit of G. Stevens, R. Pollack [7] and M. Greenberg [3] with a new unified presentation including the non-ordinary case. This…

We first briefly survey the value-distribution theory of L-functions of the Bohr-Jessen flavor (or the theory of "M-functions"). Limit formulas for the Riemann zeta-function, Dirichlet L-functions, automorphic L-functions etc. are…

We prove a strong form of the trivial zero conjecture at the central point for the $p$-adic $L$-function of a non-critically refined self-dual cohomological cuspidal automorphic representation of $\mathrm{GL}_2$ over a totally real field,…

We consider the value distribution of logarithms of symmetric square L-functions associated with newforms of even weight and prime power level at real s> 1/2. We prove that certain averages of those values can be written as integrals…

We explicitly compute the special values of the standard $L$-function $L(s, F_{12}, \mathrm{St})$ at the critical points $s\in\{-8, -6, -4, -2, 0, 1, 3, 5, 7, 9\}$, where $F_{12}$ is the unique (up to a scalar) Siegel cusp form of degree…

Langlands' functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which…

The analytic properties of automorphic L-functions have historically been obtained either through integral representations (the "Rankin-Selberg method"), or properties of the Fourier expansions of Eisenstein series (the "Langlands-Shahidi…