Metric properties of some special p-adic series expansions

Metric Properties of Engel Series Expansions of Laurent Series

ON SOME p-ADIC SERIES WITH FACTORIALS

In the last nine years p-adic numbers have been successfully applied in various branches of theoretical and mathematical physics (for a review see [1-3]). One of the objects which we often encounter is a p-adic series. My interest in p-adic series is mainly motivated by the significant role they might play not only in pure but also in applied mathematics. It was initiated in 1987 [4] by an obse...

A note on some expansions of p - adic functions

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by (φm)m∈N0 . The system (φm)m∈N0 is defined in the space C(Zp,Cp) of Cp-valued continuous functions on Zp. J. Rutkowski has also considered some questions concerning expansions of functions from C(Zp,Cp) with respect to (φm)m∈N0 . This paper is a remark to Rutkowski’s paper....

Some properties of $τ$-adic expansions on hyperelliptic Koblitz curves

This paper explores two techniques on a family of hyperelliptic curves that have been proposed to accelerate computation of scalar multiplication for hyperelliptic curve cryptosystems. In elliptic curve cryptosystems, it is known that Koblitz curves admit fast scalar multiplication, namely, the τ -adic non-adjacent form (τ -NAF). It is shown that the τ -NAF has the three properties: (1) existen...

p-ADIC PROPERTIES OF MODULAR SHIFTED CONVOLUTION DIRICHLET SERIES

Ho stein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms f1 and f2. The second two authors investigated certain special values of symmetrized sums of such functions, numbers which are generally expected to be mysterious transcendental numbers. They proved that the generating functions of these values in the h-aspect are linear combinat...