1. Introduction. A central problem in cryptography is to establish the existence of one-way
functions. Such a function would have the property that, while it is computable in polynomial …

When I started at the University of Washington in 1979, my main area of research was p-adic
analysis. I had just published a joint article with Benedict Gross about ap-adic formula for …

Let F be a global function field over a finite constant field and ∞ a place of F. The ring A of
functions regular away from ∞ in F is a Dedekind domain. For such A Goss defined a ζ …

Abstract Purpose Don Zagier suggested a natural construction, which associates a real
number and p-adic numbers for all primes p to the cusp form g= Δ of weight 12. He claimed …

R. Pellikaan (Arithmetic, Geometry and Coding Theory, Vol. 4, Walter de Gruyter, Berlin,
1996, pp. 175–184) introduced a two variable zeta-function Z (t, u) for a curve over a finite …

We define the p-density of a finite subset D⊂ Nr, and show that it gives a sharp lower bound
for the p-adic valuations of the reciprocal roots and poles of zeta functions and L-functions …

We present an efficient deterministic algorithm which outputs exact expressions in terms of n
for the number of monic degree n irreducible polynomials over F q of characteristic p for …

We present a group-theoretic criterion under which one may verify the Artin conjecture for
some (nonmonomial) Galois representations, up to finite height in the complex plane. In …

In this paper, the author presents a new approach to the subjects in the title, putting them in
a new light. In fact, only integration by parts is used. This approach has two advantages:(1) it …

Let p be a prime number. In this paper we describe p-adic properties of the special values of
the standard zeta function 9 (s, f, X), where f is a Siegel cusp form of an even degree m and …