Related papers: Classification of p-adic functions satisfying Kumm…

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…

We prove general Dwork-type congruences for Hasse--Witt matrices attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions…

We prove a version of both Jacobi's and Montel's Theorems for the case of continuous functions defined over the field $\mathbb{Q}_p$ of $p$-adic numbers. In particular, we prove that, if \[ \Delta_{h_0}^{m+1}f(x)=0 \ \ \text{for all}…

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly $p^m$ fixed points such that $\phi^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with…

This paper provides an introduction to Eisenstein measures, a powerful tool for constructing certain $p$-adic $L$-functions. First seen in Serre's realization of $p$-adic Dedekind zeta functions associated to totally real fields, Eisenstein…

We introduce new p-adic convergent functions, which we call the p-adic hypergeometric functions of logarithmic type. The first main result is to prove the congruence relations that are similar to Dwork's. The second main result is that the…

In the paper, using the extended fermionic $p$-adic integral on $\mathbb{Z}_p$, the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and…

In this article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the…

We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$-functions of congruent motives. We show that algebraic local Euler factors satisfy precise interpolation properties in…

Dress and Siebeneicher gave a significant generalization of the construction of Witt vectors, by producing for any profinite group $G$, a ring-valued functor $\mathbf{W}_G$. This paper gives a concrete interpretation of the rings…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…

In this paper, we investigate the stabilizers of certain multisets $\mod p^k$ with respect to their natural multiplicative action, completely describing them for a certain family of polynomials whenever $p$ is an odd prime. This elucidates…

We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions modulo…

For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of $p$-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We…

In this work we study $p$-adic continuous functions in several variables taking values on $\mathbb{Z}_p$. We describe the orthonormal van der Put base of these functions and study various Lipschitz conditions in several variables,…

For function spaces equipped with Muckenhoupt weights, the validity of continuous Sobolev embeddings in case $p_0\leq p_1$ is characterized. Extensions to Jawerth-Franke embeddings, vector-valued spaces and examples involving some prominent…

In this article we study $p$-adic properties of sequences of integers (or $p$-adic integers) that satisfy a linear recurrence with constant coefficients. For such a sequence, we give an explicit approximate twisted interpolation to $\mathbb…

Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ K^m let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and…

The aim of this paper is to investigate the trivial zeros of the Katz $p$-adic $L$-functions by the CM congruence. We prove the existence of trivial zeros of the Katz $p$-adic $L$-functions for general CM fields and establish a first…

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…