… 4 The field of p-adic numbers What if our p-adic number a does not satisfy lal, ≤ 1? Then we
… might try to extend f(s) = ns by continuity from nonnegative integers s to all p-adic integers s. …

… p-adic (or rather Witt vector) cohomology theories for varieties defined over fields of … A p-adic
version of a classical theorem of Borel then shows that C (t) is a quotient of two polynomials …

… that the following Zeta Functions of Finite Graphs 111 diagram, … k<n -- l), the closed path Zeta
Functions of Finite Graphs 219 which is … Zeta functions of finite multigraphs We begin with a …

… "p-adic metrie" we must enlarge the rational number field Q in a way analogous to how the
real numbers IR and then the eomplex numbers … What if our p-adic number a does not satisfy …

… study the representation zeta functions of two types of groups: compact p-adic analytic groups
… The field of p-adic numbers is denoted by Qp and the ring of p-adic integers by Zp. More …

… zeta functions by the second author, in the Lluıs Santaló Research Summer School 2019:
p-Adic Analysis, … with the ring of p-adic integers Zp (and its fraction field Qp); indeed, Zp = lim …

… For a prime number p, we use Zp, Qp, and Cp to denote the ring of p-adic integers, the
field of p-adic numbers, and the completion of an algebraic closure of Qp, respectively. Let |·|p …

… It is concerned with (p-adic) L-functions (in partially (p-adic) zeta functions) and cyclotomic
(… it is a finite extension of the field of p-adic numbers Qp. Let νK be the normalized exponential …

… As we previously pointed out, the origins of p-adic numbers can be traced to the work of …
the foundations of p-adic analysis and its application to the proof of rationality of zeta functions of …

… Batyrev proved this result using p-adic integration and the Weil Conjectures. Kontsevich ob…
of Hodge numbers. The key was to replace the p-adic integers by C[[t]], and p-adic integration …