Additive functions for number systems in function fields
نویسندگان
چکیده
منابع مشابه
Additive functions for number systems in function fields
Let Fq be a finite field with q elements and p ∈ Fq [X, Y ]. In this paper we study properties of additive functions with respect to number systems which are defined in the ring Fq [X, Y ]/p(X, Y )Fq [X, Y ]. Our results comprise distribution results, exponential sum estimations as well as a version of Waring’s Problem restricted by such additive functions. Similar results have been shown for q...
متن کاملNon-Abelian L-Functions For Number Fields
In this paper we introduce non-abelian zeta functions and more generally non-abelian L-functions for number fields, based on geo-arithmetical cohomology, geo-arithmetical truncation and Langlands’ theory of Eisenstein series. More precisely, in Chapter I, we start with a new yet natural geo-arithmetical cohomology and a geo-arithmetical stability in order to define genuine non-abelian zeta func...
متن کاملStatistics of Number Fields and Function Fields
We discuss some problems of arithmetic distribution, including conjectures of Cohen-Lenstra, Malle, and Bhargava; we explain how such conjectures can be heuristically understood for function fields over finite fields, and discuss a general approach to their proof in the function field context based on the topology of Hurwitz spaces. This approach also suggests that the Schur multiplier plays a ...
متن کاملPrime Number Theorem for Algebraic Function Fields
Elementary proofs of the abstract prime number theorem of the form A(w) = qm + 0(qmm~i) for algebraic function fields are given. The proofs use a refinement of a tauberian theorem of Bombieri. 0. Introduction The main purpose of this paper is to give elementary proofs of the abstract prime number theorem for algebraic function fields (henceforth, the P.N.T.) which was established in the author'...
متن کاملNon-Abelian Zeta Functions For Function Fields
In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields. More precisely, we first introduce new yet genuine non-abelian zeta functions for curves defined over finite fields, by a ‘weighted count’ on rational points over the corresponding moduli spaces of semi-stable vector bundles using moduli interpretation of these po...
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: Finite Fields and Their Applications
سال: 2010
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2010.02.002