A vanishing result for Igusa's p-adic zeta functions with character
نویسندگان
چکیده
منابع مشابه
A vanishing result for Igusa’s p-adic zeta functions with character
Let K be a p-adic field and let f be a K-analytic function on an open and compact subset of K3. Let R be the valuation ring of K and let χ be an arbitrary character of R×. Let Zf,χ(s) be Igusa’s p-adic zeta function. In this paper, we prove a vanishing result for candidate poles of Zf,χ(s). This result implies that Zf,χ(s) has no pole with real part less than −1 if f has no point of multiplicit...
متن کاملComputing Zeta Functions via p-Adic Cohomology
We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.
متن کاملUniform p-adic cell decomposition and local zeta functions
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 applications of our cell decomposition. A first implication is a uniform quantifier elimination for p-adic fields. Beiair [2], Delon [6] and Weispfenning [16] obtained quantifier elimination in other languages, ...
متن کاملOn p-adic multiple zeta and log gamma functions
We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...
متن کاملOn the smallest poles of Igusa’s p-adic zeta functions
Let K be a p-adic field. We explore Igusa’s p-adic zeta function, which is associated to a K-analytic function on an open and compact subset of Kn. First we deduce a formula for an important coefficient in the Laurent series of this meromorphic function at a candidate pole. Afterwards we use this formula to determine all values less than −1/2 for n = 2 and less than −1 for n = 3 which occur as ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2007
ISSN: 1370-1444
DOI: 10.36045/bbms/1195157141