Results 11 to 20 of about 714,179 (209)
Levels of Function Fields of Surfaces over Number Fields
Journal of Algebra, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jannsen, U., Sujatha, R.
openaire +3 more sources
On the Fontaine–Mazur Conjecture for Number Fields and an Analogue for Function Fields
Journal of Number Theory, 2000 The conjecture of Fontaine-Mazur says that if \(k\) is a number field, \(l\) a prime, and \(M\) an unramified \(l\)-adic analytic \(l\)-extension of \(k\), then \(M/k\) is a finite extension. This conjecture is wrong for function fields. But the authors show that, if we start with an equivalent conjecture and restrict to special cases, it is possible ...
Holden, James F., Holden, Joshua Brandon
openaire +2 more sources
Number fields and function fields: coalescences, contrasts and emerging applications [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015 The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field.
Keating, J. P. +2 more
openaire +5 more sources
On Class Number Relations over Function Fields
Journal of Number Theory, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Julie T.-Y., Yu, Jing
openaire +3 more sources
Cylotomic function fields over finite fields with class number three
, 2019 We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.
Bilhan, Mehpare +2 more
openaire +3 more sources
Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields
Journal of Algebra, 2007 Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n >= 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension >= 1 is undecidable.
Eisenträger, Kirsten
openaire +3 more sources
Classification of function fields with class number three
Journal of Pure and Applied Algebra, 2015 The aim of this paper is to give a complete classification of congruence function fields \(K/{\mathbb F}_q\) with class number \(h_K=3\). The case \(h_K=1\) was solved by \textit{R. E. MacRae} [J. Algebra 17, 243--261 (1971; Zbl 0212.53302)], \textit{M. L. Madan} and \textit{C. S. Queen} [Acta Arith.
Bilhan, Mehpare +2 more
openaire +4 more sources
A Class Number Relation Over Function Fields
Journal of Number Theory, 1995 Let \(G(m)= \sum_{dd'=m} \max d,d'\) and let \(H(d)\) be the Hurwitz class number for the discriminant \(d\); The classical Hurwitz relation [\textit{A. Hurwitz}, Math. Ann. 25, 157-196 (1885; JFM 17.0154.02)] states that \(G(m)= \sum_{\substack{ t\in \mathbb{Z}\\ t^2\leq 4m}} H(4m- t^2)\).
Yu, J.K.
openaire +3 more sources
Mathematics, 2021 In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
doaj +1 more source
Finiteness theorems for algebraic tori over function fields
Comptes Rendus. Mathématique, 2021 We present a number of finiteness results for algebraic tori (and, more generally, for algebraic groups with toric connected component) over two classes of fields: finitely generated fields and function fields of algebraic varieties over fields of type ...
Rapinchuk, Andrei S., Rapinchuk, Igor A.
doaj +1 more source