The p-adic analytic Dedekind sums
نویسندگان
چکیده
منابع مشابه
p-ADIC DEDEKIND AND HARDY-BERNDT TYPE SUMS RELATED TO VOLKENBORN INTEGRAL ON Zp
where ((x)) = x − [x]G − 1 2 , if x / ∈ Z, ((x)) = 0, x ∈ Z, where [x]G is the largest integer ≤ x cf. ([1], [5], [9], [11], [12], [13]). In this paper, Zp, Qp, Cp, C and Z, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, the p-adic completion of the algebraic closure of Qp normalized by |p|p = p −1, and the complex field and integer numbers. Let q be an ...
متن کاملAnalytic P-adic Cell Decomposition and P-adic Integrals
Roughly speaking, the semialgebraic cell decomposition theorem for p-adic numbers describes piecewise the p-adic valuation of p-adic polyno-mials (and more generally of semialgebraic p-adic functions), the pieces being geometrically simple sets, called cells. In this paper we prove a similar cell decomposition theorem to describe piecewise the valuation of analytic functions (and more generally...
متن کاملT-ADIC L-FUNCTIONS OF p-ADIC EXPONENTIAL SUMS
The T -adic deformation of p-adic exponential sums is defined. It interpolates all classical p-power order exponential sums over a finite field. Its generating L-function is a T -adic entire function. We give a lower bound for its T -adic Newton polygon and show that the lower bound is often sharp. We also study the variation of this L-function in an algebraic family, in particular, the T -adic...
متن کاملHigher Dimensional Dedekind Sums
In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...
متن کاملAnalytic vectors in continuous p-adic representations
Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...
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: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.07.022