相关论文: Derivative of the standard $p$-adic $L$-function a…

We generalize and simplify the constructions of Darmon-Rotger and Hsieh of an unbalanced triple product $p$-adic $L$-function $\mathscr{L}_p^f(\boldsymbol{f},\boldsymbol{g},\boldsymbol{h})$ attached to a triple…

Let $f$ be a primitive form of weight $2k+j-2$ for $SL_2(Z)$, and let $\mathfrak p$ be a prime ideal of the Hecke field of $f$. We denote by $SP_m(Z)$ the Siegel modular group of degree $m$. Suppose that $k \equiv 0 \mod 2, \ j \equiv 0…

We relate $p$-adic families of Jacobi forms to Big Heegner points constructed by B. Howard, in the spirit of the Gross-Kohnen-Zagier theorem. We view this as a GL(2) instance of a $p$-adic Kudla program.

Given an abelian variety $A$ over a global function field $K$ of characteristic $p>0$ and an irreducible complex continuous representation $\psi$ of the absolute Galois group of $K$, we obtain a BSD-type formula for the leading term of…

The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\Pi$ of $\mathrm{GL}(2n)$ over a totally real field $F$ admitting a Shalika model. We use a modular…

We construct the three-variable p-adic triple product L-functions attached to Hida families of ellptic newforms and prove the explicit interpolation formulae at all critical specializations by establishing explicit Ichino's formulae for the…

Let $\Pi$ be a regular algebraic cuspidal automorphic representation (RACAR) of $\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$. When $\Pi$ is $p$-nearly-ordinary for the maximal standard parabolic with Levi $\mathrm{GL}_1 \times \mathrm{GL}_2$,…

Let $\pi$ be a cuspidal, cohomological automorphic representation of an inner form $G$ of $\mathrm{PGL}_2$ over a number field $F$ of arbitrary signature. Further, let $\mathfrak{p}$ be a prime of $F$ such that $G$ is split at…

In this article, we set up a strategy to prove one divisibility towards the main Iwasawa conjecture for the Selmer groups attached to the twisted adjoint modular Galois representations associated to Hida families. This conjecture asserts…

The space of Siegel cuspforms of degree $2$ of weight $3$ with respect to the congruence subgroup $\G_2(2,4,8)$ was studied by van Geemen and van Straten in Math. computation. {\bf 61} (1993). They showed the space is generated by six-tuple…

Let $\mathbb{F}_{q}$ denote the finite field of order $q$ (a power of a prime $p$). We study the $p$-adic valuations for zeros of $L$-functions associated with exponential sums of the following family of Laurent polynomials…

This paper is a continuation of the author's previous work, where we studied the variation of the number of isomorphic classes of $G_{\mathbb{Q}}$-stable lattices in p-adic families of residually reducible ordinary Galois representations.…

In this paper, we focus on a family of generalized Kloosterman sums over the torus. With a few changes to Haessig and Sperber's construction, we derive some relative $p$-adic cohomologies corresponding to the $L$-functions. We present…

Let $G$ be a $p$-adic reductive group and $\mathfrak{g}$ its Lie algebra. We construct a functor from the extension closure of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$ associated to $\mathfrak{g}$ into the category of locally…

Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $\infty$), which interpolates the complex…

Let $G$ be a connected reductive group over a $p$-adic field $F$ of characteristic 0 and let $M$ be an $F$-Levi subgroup of $G.$ Given a discrete series representation $\sigma$ of $M(F),$ we prove that there exists a locally constant and…

Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive integer. A smooth irreducible representation of the group $GL(n,K)$ is said to be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant linear form.…

We show that Siegel modular forms of level \Gamma_0(p^m) are p-adic modular forms. Moreover we show that derivatives of such Siegel modular forms are p-adic. Parts of our results are also valid for vector-valued modular forms. In our…

We prove a compatibility theorem between the Stark conjecture and the Harris-Venkatesh conjecture for imaginary dihedral modular forms of weight $1$. The key technical input is a general two-variable $\mathrm{PGL}_2$ Siegel-Weil formula…

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L-functions in the context of the calculation of moments and connections with Random Matrix Theory. According…