Related papers: Wach modules and critical slope p-adic L-functions

Meher et al. [Proc. Amer. Math. Soc. 147 (2019)] have recently established that $L-$functions attached to certain cusp forms of half-integral weight have infinitely many zeros on the critical line. Kim [J. Numb. Th. 253 (2023)] obtained…

Let $p$ be an odd prime integer, $F/\mathbb{Q}$ be an imaginary quadratic field, and $\Psi$ be a small slope cuspidal Bianchi modular form over $F$ which is non-ordinary at $p$. In this article, we first construct a $p$-adic distribution…

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…

In this paper, we compare two different constructions of $p$-adic $L$-functions for modular forms and their relationship to Galois cohomology: one using Kato's Euler system and the other using Emerton's $p$-adically completed cohomology of…

Using the $\scr L$-invariant constructed in our previous paper we prove a Mazur-Tate-Teitelbaum style formula for derivatives of p-adic L-functions of elliptic modular forms at near central points. In the second version of the paper the…

For a crystalline p-adic representation of the absolute Galois group of Qp, we define a family of Coleman maps (linear maps from the Iwasawa cohomology of the representation to the Iwasawa algebra), using the theory of Wach modules. Let f =…

In this paper, using $p$-adic analysis and $p$-adic L-functions, we show how to extend classical congruences (due to Wilson, Gauss, Dirichlet, Jacobi, Wolstenholme, Glaisher, Morley, Lemher and other people) to modulo $p^k$ for any $k>0$.

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…

Assuming the generalized Riemann hypothesis, we prove quantitative estimates for the number of simple zeros on the critical line for the L-functions attached to classical holomorphic newforms.

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 $K$,…

We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler system associated to a quadratic Hilbert modular form. We show that this can be expressed as a value, outside the interpolation range, of the p-adic…

In this paper we recall the method of Greenberg and Stevens to calculate derivatives of p-adic L-functions using deformations of Galois representation and we apply it to the symmetric square of a modular form Steinberg at p. Under certain…

We study the theory of finite-order p-adic functions and distributions on ray class groups of number fields, and apply this to the construction of (possibly unbounded) p-adic L-functions for automorphic forms on GL(2) which may be…

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…

We revisit the proposed equality between discrete Fourier transforms of $p$-adic $\Gamma_p$--values and $p$-adic $L$--derivatives for odd characters modulo a prime $p$. The clean identity is false in general. Building on Coleman reciprocity…

In this paper, we compute the $q$-adic slopes of the L-functions of an important class of exponential sums arising from analytic number theory. Our main tools include Adolphson-Sperber's work on toric exponential sums and Wan's…

We define a two-variable $p$-adic Asai $L$-function for a finite-slope family of Hilbert modular forms over a real quadratic field (with one component of the weight, and the cyclotomic twist variable, varying independently); and a…

Let p be a prime number, and let f, g, and h be three modular forms of weights $\kappa$, $\lambda$, and $\mu$ for $SL(2,\Bbb{Z})$. We suppose $\kappa \geq \lambda + \mu$. In joint work with Kudla, one of the authors obtained a formula for…

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 under GRH that zeros of $L$-functions of modular forms of level $N$ and weight $k$ become uniformly distributed on the critical line when $N+k\to\infty.$