Results 181 to 190 of about 714,179 (209)

Analogies Between Function Fields and Number Fields

American Journal of Mathematics, 1983
Whereas Iwasawa's theory of p-cyclotomic extensions was inspired by Weil's theory of the characteristic polynomial of the Frobenius endomorphism of a function field over a finite field of constants, the authors of the present paper in turn take Iwasawa's theory as a sample for an analogous theory in the setting of function fields resp.
Mazur, B., Wiles, A.
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Statistics of Number Fields and Function Fields

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011
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.
Akshay Venkatesh, Jordan S. Ellenberg
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Number Theory in Function Fields

, 2002
Elementary number theory is concerned with arithmetic properties of the ring of integers. Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field ...
Rosen, Michael Ira(viaf)9913453
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On the Pythagoras number of function fields of curves over number fields

Israel Journal of Mathematics, 2023
For 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.
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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.
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The Sum of Digits Function In Number Fields

Bulletin of the London Mathematical Society, 1998
The 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.
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On the Zeta-Functions of Algebraic Number Fields

American Journal of Mathematics, 1947
1. 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 ...
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Units in number fields and in function fields

Expositiones Mathematicae, 1999
Number 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.
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