Searching for $p$-adic eigenfunctions

SEARCHING FOR p-ADIC EIGENFUNCTIONS

In doing p-adic analysis on spaces of classical modular functions and forms, it is convenient and traditional to broaden the notion of “modular form” to a class called “overconvergent p-adic modular forms.” Critical for the analysis of the p-adic Banach spaces composed of this wider class of forms is the “Atkin U -operator”, which is completely continuous and whose spectral theory (still not ve...

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.

$p$-adic Dual Shearlet Frames

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

p-Adic description of Higgs mechanism I: p-Adic square root and p-adic light cone

This paper is the first one in the series devoted to the calculation of particle mass spectrum in Topological GeometroDynamics. In this paper p-adic conformal field theory limit of TGD is formulated. TGD Universe is critical at quantum level and the idea is to realize criticality via conformal invariance. Ordinary real numbers do not allow this but if one assumes that in long length scales p-ad...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES