P-adic analysis and zeta functions Page 1 RIGHT: URL: CITATION: AUTHOR(S): ISSUE DATE:
TITLE: P-adic analysis and zeta functions Monsky, Paul Monsky, Paul. P-adic analysis and zeta …

Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph. D. in
mathematics at Princeton in 1974. He spent the year 1974-75 and the spring semester 1978 …

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Introduction. In this paper we shall discuss certain p-adic zeta functions, their
generalizations and new simple functional equations satisfied by them. A detailed …

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 …

We prove that the p-adic zeta-function constructed by Kubota and Leopoldt has the Dirichlet
series expansion Where the convergence of the first summation is for the p-adic topology …

These lectures are divided in three parts, almost independent part I is devoted to the more
less classical theory of valuated fields (Hensel's lemma, extension of a valuation, locally …

In [16], JP Serre developed the theory of p-adic modular forms (cf. Sect. 5) and applied it to
the construction of p-adic zeta function. In this paper, we shall try to generalize a formula for …

Let K be ap-adic field, R the valuation ring of K, P the maximal ideal of R and q the
cardinality of the residue field R/P. Let f be a polynomial over R in n> 1 variables and let χ be …

The purpose of this paper is to give a cell decomposition for p-adic fields, uniform in p. This
generalizes a cell decomposition for fixed p, proved by Denef [7],[9]. We also give some …