Results 251 to 260 of about 3,259,448 (285)
Some of the next articles are maybe not open access.
On the Pythagoras number of function fields of curves over number fields
Israel Journal of Mathematics, 2023For a field \(K\), the Pythagoras number \(p(K)\) is defined to be the smallest positive integer \(m\) such that every finite sum of squares of elements of \(K\) is a sum of \(m\) such squares, if such an integer exists, and \(\infty\) otherwise. For example, it is known that \(p(\mathbb Q(t))=5\) [\textit{Y. Pourchet}, Acta Arith.
openaire +2 more sources
Number Fields and Function Fields—Two Parallel Worlds
2005* Preface * Participants * List of Contributors * G. Bockle: Arithmetic over Function Fields: A Cohomological Approach * T. van den Bogaart and B. Edixhoven: Algebraic Stacks Whose Number of Points over Finite Fields Is a Polynomial * H. Brenner: On a Problem of Miyaoka * F. Breuer and R.
van der Geer, G., Moonen, B., Schoof, R.
openaire +3 more sources
The Sum of Digits Function In Number Fields
Bulletin of the London Mathematical Society, 1998The aim of this paper is the investigation of the sum of digits function in canonical number systems. These number systems are the natural generalization of ordinary \(q\)-adic number systems to maximal orders of number fields. In particular, we are concerned with the asymptotic description of the sum of digits function in canonical number systems.
openaire +2 more sources
On the Zeta-Functions of Algebraic Number Fields
American Journal of Mathematics, 19471. It was proved by E. Artin 1 that if k is an algebraic number field (of finite degree) and K a normal extension field with the icosahedral group as the Galois group with regard to k, then the zeta-function g (s, kc) of k divides the zeta-function g(s, K), in the sense that the quotient t (s, K) /g (s, kc) is an integral function of the complex ...
openaire +2 more sources
Units in number fields and in function fields
Expositiones Mathematicae, 1999Number fields on the one hand and congruence function fields on the other hand share similar properties. For curves over an arbitrary field we have a behavior different from the case of number fields or function fields over a finite field. In this paper, it is considered a question raised by \textit{M. Miyanishi} [J. Algebra 173, No.
openaire +2 more sources
The Moments of the Sum-Of-Digits Function in Number Fields
Canadian Mathematical Bulletin, 1999AbstractWe consider the asymptotic behavior of the moments of the sum-of-digits function of canonical number systems in number fields. Using Delange’s method we obtain the main term and smaller order terms which contain periodic fluctuations.
Gittenberger, Bernhard +1 more
openaire +2 more sources
On zeta-functions of algebraic number fields
1968Let \(\lambda_1, \lambda_2\) be unramified Hecke characters of fields \(k_1,k_2\) respectively. Suppose that \((k_1k_2:Q) = (k_1:Q)(k_2:Q)\). Denote by \(\zeta_{k_1k_2}(s;\lambda_1, \lambda_2)\) the scalar product of Hecke \(\zeta\)-functions \(\zeta_{k_1}(s;\lambda_1)\) and \(\zeta_{k_2}(s; \lambda_2)\) [cf. \textit{A. I. Vinogradov}, Izv. Akad.
openaire +2 more sources
Analogies between number fields and function fields
2001Ichiro Satake +4 more
openaire +1 more source
A Field Of Functions Isomorphic To The Field Of Real Numbers
The European Proceedings of Social and Behavioural Sciences, 2019openaire +1 more source
On automorphism groups of cyclotomic function fields over finite fields
Journal of Number Theory, 2016Liming, Chaoping Xing
exaly