Related papers: Unitary Friedberg--Jacquet periods and anticycloto…

Let $E$ be a rational elliptic curve and let $p$ be an odd prime of additive reduction. Let $K$ be an imaginary quadratic field and fix a positive integer $c$ prime to the conductor of $E$. The main goal of the present article is to define…

We establish a relation between intersection numbers of special cycles on a Shimura curve and special values of derivatives of metaplectic Eisenstein series at a place of bad reduction where p-adic uniformization in the sense of Cherednik…

We build a one-variable $p$-adic $L$-function attached to two Hida families of ordinary $p$-stabilised newforms $\mathbf{f}$, $\mathbf{g}$, interpolating the algebraic part of the central values of the complex $L$-series $L(f \otimes…

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators…

We construct differential operators for families of overconvergent Hilbert modular forms by interpolating the Gauss--Manin connection on strict neighborhoods of the ordinary locus. This is related to work done by Harron and Xiao and by…

We produce a flat $\Lambda$-module of $\Lambda$-adic critical slope overconvergent modular forms, producing a Hida-type theory that interpolates such forms over $p$-adically varying integer weights. This provides a Hida-theoretic…

Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by…

In this work we study the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms of higher index, generalizing previous results of Arakawa and Murase. Furthermore, we obtain algebraicity results on special…

We construct a five-variable $p$-adic $L$-function attached to Hida families on the definite unitary groups $U(3)$ and $U(2)$ by using the Ichino-Ikeda formula. The interpolation formula fits into the conjectural shape of $p$-adic…

We give a construction of $p$-adic Asai $L$-functions for cohomological cuspidal automorphic representations of ${\rm GL}_2$ over CM fields. If the base field is imaginary quadratic, Loeffler-Williams recently constructed the $p$-adic Asai…

Modular and mock modular forms possess many striking $p$-adic properties, as studied by Bringmann, Guerzhoy, Kane, Kent, Ono, and others. Candelori developed a geometric theory of harmonic Maass forms arising from the de Rham cohomology of…

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…

Let $F$ be a totally real field and let $E/F$ be a CM quadratic extension. We construct a $p$-adic $L$-function attached to Hida families for the group ${\rm GL}_{2/F}\times {\rm Res}_{E/F}{\rm GL}_{1}$. It is characterised by an exact…

Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic methods to prove the existence of analytic continuations of $\zeta$ and $L$ functions. These methods have become considerably more sophisticated in recent years, and…

The purpose of this article is to establish theories concerning $p$-adic analogues of Hodge cohomology and Deligne-Beilinson cohomology with coefficients in variations of mixed Hodge structures. We first study log overconvergent…

We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic p-adic L-functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach…

On a smooth, compact, $n$-dimensional Riemannian manifold, we consider functions $u_h$ that are joint quasimodes of two semiclassical pseudodifferential operators $p_1(x,hD)$ and $p_2(x,hD)$. We develop $L^p$ estimates for $u_h$ when the…

This is a report for the author's talk in ICM-2018. Motivated by the formulas of Gross--Zagier and Waldspurger, we review conjectures and theorems on automorphic period integrals, special cycles on Shimura varieties, and their connection to…

We generalise Pollack's construction of plus/minus L-functions to certain cuspidal automorphic representations of $\mathrm{GL}_{2n}$ using the $p$-adic $L$-functions constructed in forthcoming work of Barrera, Dimitrov and Williams.

The purpose of this semi-expository article is to give another proof of a classical theorem of Shimura on the critical values of the standard L-function attached to a Hilbert modular form. Our proof is along the lines of previous work of…