共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the Jacobians of the genus 3 Picard and Fermat curves with respect to the problem of maximizing the minimum non-zero
norm. We use criteria for symplectic lattices related to the criteria of perfect and eutactic for classical lattices. We show
that the Picard curve is a local maximum, but the Fermat curve is not. 相似文献
2.
本文旨在介绍Fermat最后定量的历史和Wiles最近所给的证明。首先简介了其在代数数论的发展过程中所起的作用,然后介绍椭圆曲线的基本概念,叙述Taniyama-Weil猜想,即任一椭圆曲线都是模的。进而介绍Ribet的工作。他证明了若Taniyama-Weil猜想对半稳定的椭圆曲线成立则Fermat最后定理成立。最后介绍了l-adic Galois表示的概念及Wiles定理,即半稳定的椭圆曲线都 相似文献
3.
Pavlos Tzermias 《Archiv der Mathematik》2010,95(1):19-24
We prove that the torsion part of the Mordell–Weil group of the Jacobian of a Fermat curve over a cyclotomic field is contained
in the kernel of a certain isogeny. This provides a natural analogue of a similar result on Jacobians of Fermat quotient curves. 相似文献
4.
Hironobu Maeda 《manuscripta mathematica》1986,56(3):333-342
Let p be an odd prime and F the Fermat curve of degree p, defined by xp+yp=1 over . Although the curve F has bad reduction at the prime (p), the stable reduction theorem assures that over some number field K/ we can get stable reduction of the curve F at the primes lying above p. We have determined it in this paper. See Abb.1. 相似文献
5.
Pavlos Tzermias 《Transactions of the American Mathematical Society》2004,356(3):939-951
We investigate low-degree points on the Fermat curve of degree 13, the Snyder quintic curve and the Klein quartic curve. We compute all quadratic points on these curves and use Coleman's effective Chabauty method to obtain bounds for the number of cubic points on each of the former two curves.
6.
Saeed Tafazolian 《Finite Fields and Their Applications》2010,16(1):1-3
In this article we provide a characterization of maximal and minimal Fermat curves using the classification of supersingular Fermat curves. 相似文献
7.
8.
Summary
In this paper existence and multiplicity results for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds are proved under intrinsic assumptions. Such results are obtained using an extension to Lorentzian Geometry of the classical Fermat principle in optics. The results are proved using critical point theory on infinite dimensional manifolds. An application to the gravitational lens effect is presented. 相似文献
9.
Pavlos Tzermias 《manuscripta mathematica》1998,97(4):483-488
We determine all algebraic points of degree at most five over Q on the Fermat curve of degree seven.
Received: 26 February 1998 / Revised version: 1 June 1998 相似文献
10.
Noriyuki Otsubo 《Journal of Number Theory》2011,131(4):648-660
We compare two calculations due to Bloch and the author of the regulator of an elliptic curve with complex multiplication which is a quotient of a Fermat curve, and express the special value of its L-function at s=0 in terms of special values of generalized hypergeometric functions. 相似文献
11.
Ken-Ichiro Kimura 《K-Theory》1996,10(1):73-82
Two linearly independent elements of k
2 of a certain quotient of a Fermat curve is exhibited in an explicit manner. The covolume of the regulator and the value of the L-function of the curve is numerically computed, and their ratio is nearly equal to a simple rational number. 相似文献
12.
Rin Sugiyama 《Journal of Number Theory》2013,133(4):1194-1206
We give a necessary and sufficient condition in terms of a matrix for which all Tate classes are Lefschetz for simple abelian varieties over an algebraic closure of a finite field. As an application, we prove under an assumption that all Tate classes are Lefschetz for simple factors of the Jacobian variety of a Fermat curve of prime degree. 相似文献
13.
Riccardo Re 《Finite Fields and Their Applications》2009,15(4):450-467
We give formulas for the genera of all the possible quotient of a Fermat curve by a group of automorphisms in characteristic zero and for many classes of quotient curves also in positive characteristic. We use those results for giving evidence to the conjecture that, in any fixed positive characteristic, there should exist supersingular curves for any genus. 相似文献
14.
In this article we recall how to describe the twists of a curve over a finite field and we show how to compute the number of rational points on such a twist by methods of linear algebra. We illustrate this in the case of plane quartic curves with at least 16 automorphisms. In particular we treat the twists of the Dyck–Fermat and Klein quartics. Our methods show how in special cases non-Abelian cohomology can be explicitly computed. They also show how questions which appear difficult from a function field perspective can be resolved by using the theory of the Jacobian variety. 相似文献
15.
Masaaki Homma 《Geometriae Dedicata》1994,53(3):287-296
We are interested in a particular geometry of plane curves in characteristicp>0, which was inspired by Thas's article [13]. We will prove that any plane curve of degree > 2 whose tangent lines at collinear points are concurrent is either a strange curve or projectively equivalent to the Fermat curve of degreeq + 1, whereq is a power ofp. 相似文献
16.
Bau-Sen Du 《Journal of Number Theory》2003,98(1):172-183
In this paper, we discuss the relationship among the generalized Fermat, double Fermat, and Newton sequences. In particular, we show that every double Fermat sequence is a generalized Fermat sequence, and the set of generalized Fermat sequences, as well as the set of double Fermat sequences, is closed under term-by-term multiplication. We also prove that every Newton sequence is a generalized Fermat sequence and vice versa. Finally, we show that double Fermat sequences are Newton sequences generated by certain sequences of integers. An approach of symbolic dynamical systems is used to obtain congruence identities. 相似文献
17.
Amnon Besser 《Israel Journal of Mathematics》2006,151(1):53-59
We give a short proof of a formula of de Shalit, expressing the cup product of two vector-valued one-forms of the second kind
on a Mumford curve in terms of Coleman integrals and residues. The proof uses the notion of double indices on curves and their
reciprocity laws. 相似文献
18.
IfPis an irreducible element of a polynomial ring over a finite field, then one can define a Fermat quotient function associated toP. This is the direct analog of the traditional Fermat quotient function defined over the rational numbers using Fermat's “little” theorem. This paper provides answers for several of the central questions about the Fermat quotients over function fields. 相似文献
19.
20.
In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular
we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover, we
define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime.
We shall study the influence of the Fermat metric on the causal properties of the spacetime, mainly the global hyperbolicity.
Moreover, we study the relations between the energy functional of the Fermat metric and the Fermat principle for the light
rays in the spacetime. This allows one to obtain existence and multiplicity results for light rays, using the Finsler theory.
Finally the case of timelike geodesics with fixed energy is considered. 相似文献