Related papers: A note on Fermionic p-adic integrals on Zp and umb…

Using the theory of $(\phi,\Gamma)$-modules and the formalism of Selmer complexes we construct the p-adic height for p-adic representations with coefficients in an affinoid algebra over $Q_p$.

We show that the number Z of q-edge-colourings of a simple regular graph of degree q is deducible from functions describing dimers on the same graph, viz. the dimer generating function or equivalently the set of connected dimer correlation…

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…

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact…

In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…

In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell…

This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

Recent innovations in the differential calculus for functions of non-commuting variables, beginning with a quaternionic variable, are now extended to consider some integration.

In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.

We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are…

Inspired by several alternative definitions of continued fraction expansions for elements in $\mathbb Q_p$, we study $p$-adically convergent periodic continued fractions with partial quotients in $\mathbb Z[1/p]$. To this end, following a…

Recent developments regarding index and overlap construction for staggered fermions are reviewed, highlighting the surprising and unexpected aspects.

In this paper, we study the parallel cases of Zagier's and Folsom-Ono's grids of weakly holomorphic (resp. weakly holomorphic and mock modular) forms of weights 3/2 and 1/2, investigating their $p$-adic properties under the action of Hecke…

In this note, we observe several properties of arithmetic divisors on the projective line over Z and give their Zariski decompositions.

Let D be a quaternion division algebra over a totally real number field F which splits exactly at one infinite place. We assume that there is a p-adic place where D doesn't split. Then the associated Shimura curve has a Cherednik…

We review various aspects of a fermionic gauge symmetry, known as the $\kappa$--symmetry, which plays an important role in formulations of superstrings, supermembranes and higher dimensional extended objects. We also review some aspects of…

In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.

We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.

These notes give a basic introduction to the theory of $p$-adic and motivic zeta functions, motivic integration, and the monodromy conjecture.