http://biblioteca.universia.net/verColeccion.do?id=8468 Mostrando recursos 1 - 20 de 66,283 es http://biblioteca.universia.net/img/logotipo.jpg http://biblioteca.universia.net/ http://biblioteca.universia.net/ficha.do?id=20814361 For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive integer whose squareroot has a continued fraction expansion with period $n+1$ lies in the range of exactly one of these polynomials. Moreover, each of these polynomials satisfy a polynomial Pell's equation $C_{i}^{2} -F_{i}H_{i}^{2} = (-1)^{n-1}$ (where $C_{i}$ and $H_{i}$ are polynomials in the v... Laughlin, James Mc http://biblioteca.universia.net/ficha.do?id=20814861 In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn and using an arithmetic Bezout theorem. This paper is a generalization, where we show that combining the methods of that paper with the theory of Chow forms leads to similar results for flat, equidimensional, integral, closed subschemes of arbitrary codimensi... Erne, Reinie http://biblioteca.universia.net/ficha.do?id=20815059 Let $p, q$ be twin prime numbers with $q-p=2$ . Consider the elliptic curves E=E_\sigma: y^2 = x (x+\sigma p)(x+\sigma q) . (\sigma =\pm 1). E=E_\sigma is also denoted as E_+ or E_- when \sigma = +1or $-1.Here the Mordell-Weil group and the rank of the elliptic curve E over the Gauss field K=Q(\sqrt -1) (and over the rational field Q is determined in several cases; and results on solutions of related Diophantine equations and simultaneous Pellian equations will be given. The arithmetic constr... Qiu, DeRong; Zhang, Xianke http://biblioteca.universia.net/ficha.do?id=20815060 The theory of continued fractions of functions $ \sqrt D $ is used to give lower bound for class numbers $h(D)$ of general real quadratic function fields $K=k(\sqrt D)$ over $k={\bf F}_q(T)$. For five series of real quadratic function fields $K$, the bounds of $h(D)$ are given more explicitly, e.g., if $ D=F^2+c,$ \mbox{}\hspace{0.1cm} then $ h(D)\geq {deg}F /{deg} P;$ \hspace{0.1cm} if $D=(SG)^2+cS, $ then $ h(D)\geq {deg}S / {deg} P; $ if $D=(A^m+a)^2+A, $ then $ h(D)\geq {deg}A / {deg} P, ... Wang, Kunpeng; Zhang, Xianke http://biblioteca.universia.net/ficha.do?id=20815061 Here we study algebraic function fields K, give necessary and sufficient condition for the ideal class group $H(K)$ of any real quadratic function field $K$ to have a cyclic subgroup of order $n$, and obtain eight series of such fields $K$, with four of them NOT ERD-type or GERD-type. Wang, KunPeng; Zhang, Xianke http://biblioteca.universia.net/ficha.do?id=20815348 This paper proves the general rank one case of Dwork's conjecture over the affine space. It generalizes and improves the method of ANT-0141 "Dwork's conjecture on unit root zeta functions" (Ann. Math., 150(1999), 867-929). In addition, explicit information about the zeros and poles (along the Gouv\^ea-Mazur conjecture direction) for the unit root zeta function is obtained. The paper is to appear in JAMS. Wan, Daqing http://biblioteca.universia.net/ficha.do?id=20815349 This is the final version of ANT-0142 ("An embedding approach to Dwork's conjecture"). It reduces the higher rank case of the conjecture over a general base variety to the rank one case over the affine space. The general rank one case is completed in ANT-0235 "Rank one case of Dwork's conjecture". Both papers will appear in JAMS. Wan, Daqing http://biblioteca.universia.net/ficha.do?id=20815350 We extend the notion of a tame covering of a pair (X,D) where X is a regular scheme and D is a normal crossing divisor (cf. SGA1), to pairs (X,Y) where X is an arbitrary scheme and Y is a closed subset in X. We show that the abelianized tame fundamental group of a regular scheme which is flat and of finite type over Spec(Z) is finite and does not depend on the choice of a particular compactification. Schmidt, Alexander http://biblioteca.universia.net/ficha.do?id=20815351 The free profinite product of finitely many absolute Galois group is an absolute Galois group. Haran, Dan; Jarden, Moshe; Koenigsmann, Jochen http://biblioteca.universia.net/ficha.do?id=20815586 This is an expository paper which gives a simple arithmetic introduction to the conjectures of Weil and Dwork concerning zeta functions of algebraic varieties over finite fields. A number of further open questions are raised. Wan, Daqing http://biblioteca.universia.net/ficha.do?id=20815588 By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well known rationality theorem. In general, the partial zeta function is probably not rational. But a theorem of Faltings says that the partial zeta function is always nearly rational. Wan, Daqing http://biblioteca.universia.net/ficha.do?id=20815589 Let A be an arbitrary ring. We introduce a Dennis trace map mod n, from K_1(A;Z/n) to the Hochschild homology group with coefficients HH_1(A;Z/n). If A is the ring of integers in a number field, explicit elements of K_1(A,Z/n) are constructed and the values of their Dennis trace mod n are computed. If F is a quadratic field, we obtain this way non trivial elements of the ideal class group of A. If F is a cyclotomic field, this trace is closely related to Kummer logarithmic derivatives; this t... Karoubi, Max; Lambre, Thierry http://biblioteca.universia.net/ficha.do?id=20815779 In this paper we prove Greenberg's pseudo-null conjecture for the field of p-th roots of unity in the case that p exactly divides the class number and the index of the global units in the local units. We also generalize to the case of multiple Z_p-extensions a theorem of Iwasawa on the Kummer extension of the cyclotomic Z_p-extension generated by p-power roots of units . McCallum, William G. http://biblioteca.universia.net/ficha.do?id=20815781 Fontaine and Mazur conjecture that a number field k has no infinite unramified Galois extension such that its Galois group is a p-adic analytic pro-p-group. We consider this conjecture for the maximal unramified p-extension of a CM-field k. Wingberg, Kay http://biblioteca.universia.net/ficha.do?id=20815783 By two well-known results, one of Ax, one of Lubotzky and van den Dries, a profinite group is projective iff it is isomorphic to the absolute Galois group of a pseudo-algebraically closed field. This paper gives an analogous characterization of relatively projective profinite groups as absolute Galois groups of regularly closed fields. Koenigsmann, Jochen http://biblioteca.universia.net/ficha.do?id=20816014 We remove the assumption "let p be odd or k totally imaginary" from several well-known theorems in Galois cohomology of number fields. For example, we show that the Galois group of the maximal extension of a number field k which is unramified outside 2 has a finite cohomological 2-dimension (also if k has real places). (The dvi-file requires the xypic-package) Schmidt, Alexander http://biblioteca.universia.net/ficha.do?id=20816320 In this paper we introduce a new method for finding Galois groups by computer. This is particularly effective in the case of Galois groups of p-extensions ramified at finitely many primes but unramified at the primes above p. Such Galois groups have been regarded as amongst the most mysterious objects in number theory. Very little has hitherto been discovered regarding them despite their importance in studying p-adic Galois representations unramified at p. The conjectures of Fontaine-Mazur sa... Boston, Nigel; Leedham-Green, Charles http://biblioteca.universia.net/ficha.do?id=20816321 Much work has gone into matrix representations of Galois groups, but there is a whole new class of naturally occurring representations that have as yet gone almost unnoticed. In fact, it is well-known in various areas of mathematics that the main sources of totally disconnected groups are matrix groups over local fields AND automorphism groups of locally finite trees. It is perhaps surprising then that representations of Galois groups into the latter have been almost ignored, while at the sam... Boston, Nigel http://biblioteca.universia.net/ficha.do?id=20816322 There are many results on the minimum distance of a cyclic code of the form that if a certain set T is a subset of the defining set of the code, then the minimum distance of the code is greater than some integer t. This includes the BCH, Hartmann-Tzeng, Roos, and shift bounds and generalizations of these. In this paper we define certain projective varieties V(T,t) whose properties determine whether, if T is in the defining set, the code has minimum distance exceeding t. Thus our attention shi... Boston, Nigel http://biblioteca.universia.net/ficha.do?id=20816915 We use a new idea to construct a theory of iterated Coleman functions in higher dimensions than 1. A Coleman function in this theory consists of a unipotent differential equation, a section on the underlying bundle and a solution to the equation on a residue disc. The new idea is to use the theory of Tannakian categories and the action of Frobenius to anlytically continue solutions of the differential equation to all residue discs. Besser, Amnon