Related papers: Factorisation of two-variable p-adic L-functions

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

We consider arbitrary algebraic families of lower order deformations of nondegenerate toric exponential sums over a finite field. We construct a relative polytope with the aid of which we define a ring of coefficients consisting of p-adic…

We construct $p$-adic $L$-functions interpolating the critical values of the degree eight $L$-functions of ${\rm GSp}(4)\times {\rm GL}(2)$ for cuspidal automorphic representations generated by $p$-ordinary Siegel modular forms of genus two…

In this brief essay a construction of the $2$-variable L-function of Langlands is sketched in terms of monomial resolutions of admissible representations of reductive locally $p$-adic Lie groups.

The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue…

In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered…

The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing…

The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the $p$-adic $L$-function of a modular form. In this paper, we give an analogue of their results for…

We study the derivative of the standard $p$-adic $L$-function associated with a $P$-ordinary Siegel modular form (for $P$ a parabolic subgroup of $\mathrm{GL}(n)$) when it presents a semi-stable trivial zero. This implies part of…

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…

We construct a Hecke-equivariant pairing on the overconvergent cohomology of Bianchi threefolds. Applying the strategy of Kim and Bella\"iche, we use this pairing to construct $p$-adic adjoint $L$-functions for Bianchi cuspforms and show…

We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of…

Radziwill and Soundararajan unveiled a connection between low-lying zeros and central values of $L$-functions, which they instantiated in the case of quadratic twists of an elliptic curve. This paper addresses the case of the family of…

In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of ad\'elic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances…

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 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 show that the class of $\mathcal{L}$-constructible functions is closed under integration for any $P$-minimal expansion of a $p$-adic field $(K,\mathcal{L})$. This generalizes results previously known for semi-algebraic and sub-analytic…

We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of…

We give a proof of the existence of Asai, exterior square, and symmetric square local $L$-functions, $\gamma$-factors and root numbers in characteristic $p$, including the case of $p = 2$. Our study is made possible by developing the…

Let E/Q be an elliptic curve with good supersingular reduction at p with a_p(E)=0. We give a conjecture on the existence of analytic plus and minus p-adic L-functions of E over the Zp-cyclotomic extension of a finite Galois extension of Q…