Related papers: Critical slope p-adic L-functions of CM modular fo…

We develop a variant of Coleman and Perrin Riou's methods giving, for a de Rham $p$-adic Galois representation, a construction of $p$-adic $L$ functions from a compatible system of global elements. As a result, we construct analytic…

Let $\rho$ be a conjugate-symplectic, geometric representation of the Galois group of a CM field. Under the assumption that $\rho$ is automorphic, even-dimensional, and of minimal regular Hodge--Tate type, we construct an Euler system for…

The use of overconvergent cohomology in constructing $p$-adic $L$-functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been established in a number of settings. The method is compatible…

Consider elliptic curves $ E:\ y^{2} = x^{3} + D^{3} $ defined over the quadratic field $\ \Q(\sqrt{-3}) $. Hecke $ L-$series attached to $ E $ are studied, formulae for their values at $ s=1, $ and bound of 3-adic valuations of these…

By $p$-adically interpolating the branching law for the spherical pair $\left(U_n, U_{n+1} \times U_{n}\right)$ of definite unitary groups, we construct a $p$-adic $L$-function attached to cohomological automorphic representations of…

We discuss several congruences satisfied by the coefficients of meromorphic modular forms, or equivalently, the $p$-adic behaviors of meromorphic modular forms under the $U_p$ operator, that are summarized from numerical experiments. In the…

We study Rubin's variant of the $p$-adic Birch and Swinnerton-Dyer conjecture for CM elliptic curves concerning certain special values of the Katz two-variable $p$-adic $L$-function that lie outside the range of $p$-adic interpolation.

We prove a Weyl-type subconvexity bound for the central value of the $L$-function of a Hecke-Maass form or a holomorphic Hecke eigenform twisted by a quadratic Dirichlet character, uniform in the archimedean parameter as well as the…

When the branch character has root number -1, the corresponding anticyclotomic Katz p-adic L-function identically vanishes. In this case, we study the $\mu$-invariant of the cyclotomic derivative of Katz p-adic L-function. As an…

For motives associated with Fermat curves, there are elements in motivic cohomology whose regulators are written in terms of special values of generalized hypergeometric functions. Using them, we verify the Beilinson conjecture numerically…

In this article, we follow Hida's approach to study the mu-invariant of the anticyclotomic projection of p-adic Hecke L-functions for CM fields along a branch character. We prove a conjecture of Gillard on the vanishing of the mu-invariant…

Let f be a modular form of weight k>=2 and level N, let K be a quadratic imaginary field, and assume that there is a prime p exactly dividing N. Under certain arithmetic conditions on the level and the field K, one can attach to this data a…

In a groundbreaking paper, T. Fukaya and K. Kato proved a slight weakening of a conjecture of the author's relating modular symbols and cup products of cyclotomic units under an assumption that a Kubota-Leopoldt p-adic L-function has no…

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…

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 $K$,…

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…

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. As an…

Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli…

Let $f$ be a modular form which is non-ordinary at $p$. Kim and Loeffler have recently constructed two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, they showed that, as in the one-variable case, Pollack's…

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…