Related papers: Plus/Minus $p$-adic $L$-functions for $\mathrm{GL}…

We show that the special values at tuples of positive integers of the $p$-adic multiple $L$-function introduced by the first-named author et al. can be expressed in terms of the cyclotomic multiple harmonic values introduced by the…

Plectic points were introduced by Fornea and Gehrmann as certain tensor products of local pointson elliptic curves over arbitrary number fields $F$. In rank $r\leq [F:\mathbb{Q}]$-situations, they conjecturally come from p-adic regulators…

We prove a conjecture of B. Gross and D. Prasad about determination of generic $L$-packets in terms of the analytic properties of the adjoint $L$-function for $p$-adic general even spin groups of semi-simple ranks 2 and 3. We also…

Let $F$ be a number field, and $\pi$ a regular algebraic cuspidal automorphic representation of $\mathrm{GL}_N(\mathbb{A}_F)$ of symplectic type. When $\pi$ is spherical at all primes $\mathfrak{p}|p$, we construct a $p$-adic $L$-function…

Let $K$ be an imaginary quadratic field. In this article, we construct $p$-adic $L$-functions of non-cuspidal Bianchi modular forms by introducing the notions of $C$-cuspidality and partial Bianchi modular symbols. When $p$ splits in $K$,…

In this paper we establish a very flexible and explicit Voronoi summation formula. This is then used to prove an almost Weyl strength subconvexity result for automorphic $L$-functions of degree two in the depth aspect. That is, looking at…

Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study…

In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this…

We construct the two-variable $p$-adic $q$-$L$-function which interpolates the generalized $q$-Bernoulli polynomials associated with primitive Dirichlet character $\chi$. Indeed, this function is the $q$-extension of two-variable $p$-adic…

This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a…

We construct four-variable $p$-adic $L$-functions for cuspidal Hida families on ${\rm GSp}(4)\times{\rm GL}(2)$ and prove a complete interpolation formula. The archimedean zeta integrals are computed by using a partial interpolation formula…

$L$-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of $\textrm{GL}(n)$, as first described by Langlands. Conjecturally these two…

Let $\pi$ be a unitary automorphic cuspidal representation of $GL_2(\mathbb{Q}_\mathbb{A})$ with Fourier coefficients $\lambda_\pi(n)$. Asymptotic expansions of certain sums of $\lambda_\pi(n)$ are proved using known functorial liftings…

The (Deuring-Heilbronn-) Linnik phenomenon is extended to L-functions associated with real analytic automorphic forms. The repelling effect of exceptional zeros of Dirichlet L-functions are felt not only by those L-functions themselves but…

It is shown that Mellin transforms of p-adic Whittaker functions exist for generic characters. For good choices of vectors they are rational functions. For class one vectors they can be calculated explicitly. It turns out that they are…

We prove explicit formulas for the $p$-adic $L$-functions of totally real number fields and show how these formulas can be used to compute values and representations of $p$-adic $L$-functions.

We extend the dictionary between Fontaine rings and $p$-adic functionnal analysis, and we give a refinement of the $p$-adic local Langlands correspondence for principal series representations of ${\rm GL}_2(\mathbf{Q}_p)$.

This is the text of a talk to the study week on \emph{Modular forms and Galois representations} held in Luminy, 1997. We give a survey of $p$-adic modular forms, as developped by Serre, Katz, Hida, Wiles, Coleman and others...

We introduce a geometric formalism for studying modular forms of half-integral weight and explore some of its basic properties. Geometric Hecke operators are constructed and some basic spaces of $p$-adic forms are introduced. The $p$-adic…

In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.