Diophantine Inheritance for $p$-adic measures

Simultaneous Diophantine Approximation in Non-degenerate p-adic Manifolds

S-arithmetic Khintchine-type theorem for products of non-degenerate analytic p-adic manifolds is proved for the convergence case. In the padic case the divergence part is also obtained. 1

p-Adic Measures and Bernoulli Numbers

Singular p-adic transformations for Bernoulli product measures

Ergodic properties of p-adic transformations have been studied with respect to Haar measure. This paper extends the study of these properties to measures beyond Haar measure. Under these measures, coefficients do not appear in equal proportions. Adding a rational number that is not an integer then takes likely strings of coefficients to one of two unlikely strings of coefficients. It follows fr...

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

An introduction to Skolem’s p-adic method for solving Diophantine equations

In this thesis, an introduction to Skolem’s p-adic method for solving Diophantine equations is given. The main theorems that are proven give explicit algorithms for computing bounds for the amount of integer solutions of special Diophantine equations of the kind f(x, y) = 1, where f ∈ Z[x, y] is an irreducible form of degree 3 or 4 such that the ring of integers of the associated number field h...