共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
Darrin Doud 《manuscripta mathematica》1998,95(4):463-469
We present an algorithm which uses the analytic parameterization of elliptic curves to rapidly calculate torsion subgroups,
and calculate its running time. This algorithm is much faster than the “traditional” Lutz–Nagell algorithm used by most computer
algebra systems to calculate torsion subgroups.
Received: 7 August 1997 / Revised version: 28 November 1997 相似文献
3.
Manfred Kolster 《Mathematische Annalen》2002,323(4):667-692
Let E be a totally complex abelian number field with maximal real subfield F, and let denote the non-trivial character of . Similar to the classical case n=1 the value of the Artin L-function at for odd is given by a relative class number formula of the form
Here is a higher Q-index, which is equal to 1 or 2 and is a higher relative class number. Here for any number field L the higher class number is the order of the finite group
closely related to the order of the higher K-theory group of the ring of integers in L.
Received: 4 June 1999 / Revised version: 27 September 2001 / Published online: 26 April 2002 相似文献
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5.
Max Gebhardt 《manuscripta mathematica》2002,107(1):89-99
We consider certain decomposition fields in extensions of ?q (Z) by the Carlitz module and give formulas for their genera and numbers of rational places, suitable for automatic computations.
By extensive calculations we found some function fields which have more rational places than the known examples of the respective
genus.
Received: 7 September 2001/ Revised version: 19 October 2001 相似文献
6.
Stéphane Louboutin 《manuscripta mathematica》2001,106(4):411-427
Let \lcub;K
m
}
m
≥ 4 be the family of non-normal totally real cubic number fields associated with the Q-irreducible cubic polynomials P
m
(x) =x
3−mx
2−(m+1)x− 1, m≥ 4. We determine all these K
m
's with class numbers h
m
≤ 3: there are 14 such K
m
's. Assuming the Generalized Riemann hypothesis for all the real quadratic number fields, we also prove that the exponents
e
m
of the ideal class groups of these K
m
go to infinity with m and we determine all these K
m
's with ideal class groups of exponents e
m
≤ 3: there are 6 suchK
m
with ideal class groups of exponent 2, and 6 such K
m
with ideal class groups of exponent 3.
Received: 16 November 2000 / Revised version: 16 May 2001 相似文献
7.
Thomas Müller 《manuscripta mathematica》2000,103(4):513-540
Let X denote a compact subset of ℝ
n
and B the unit ball in ℝ
n
. In this paper we investigate analytical and topological compactness properties of minimizing sequences for the n-energy in the class of maps , the homotopy class .
Received: 5 June 2000 相似文献
8.
Summary. Here the stability and convergence results of oqualocation methods providing additional orders of convergence are extended
from the special class of pseudodifferential equations with constant coefficient symbols to general classical pseudodifferential
equations of strongly and of oddly elliptic type. The analysis exploits localization in the form of frozen coefficients, pseudohomogeneous
asymptotic symbol representation of classical pseudodifferential operators, a decisive commutator property of the qualocation
projection and requires qualocation rules which provide sufficiently many additional degrees of precision for the numerical
integration of smooth remainders. Numerical examples show the predicted high orders of convergence.
Received January 29, 1998 / Published online: June 29, 1999 相似文献
9.
Andrei Yafaev 《manuscripta mathematica》2001,104(2):163-171
Let S
1 and S
2 be two Shimura curves over ℚ attached to rational indefinite quaternion algebras B
1 ℚ and B
1 ℚ with maximal orders B
1 and B
2 respectively. We consider an irreducible closed algebraic curve C in the product (S
1×S
2)ℂ such that C(ℂ) ∩ (S
1×S
2)(ℂ) contains infinitely many complex multiplication points. We prove, assuming the Generalized Riemann Hypothesis (GRH) for
imaginary quadratic fields, that C is of Hodge type.
Received: 3 January 2000 / Revised version: 2 October 2000 相似文献
10.
Gregory J. Pearlstein 《manuscripta mathematica》2000,102(3):269-310
Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural
Higgs bundle structure which is invariant under the ℂ* action studied in [20]. We then specialize our construction to the context of [6], and show that the resulting Higgs field
θ determines (and is determined by) the Gromov–Witten potential of the underlying family of Calabi–Yau threefolds.
Received: 14 February 2000 相似文献
11.
Ribet [Ri] has generalized the conjecture of Shimura–Taniyama–Weil to abelian varieties defined over Q,giving rise to the study of abelian varieties of GL2-type. In this context, all curves over Q of genus one have Jacobian variety of GL2-type. Our aim in this paper is to begin with the analysis of which curves of genus 2 have Jacobian variety of GL2-type. To this end, we restrict our attention to curves with rational Rosenhain model and non-abelian automorphism group,
and use the embedding of this group into the endomorphism algebra of its Jacobian variety to determine if it is of GL2-type.
Received: 31 March 1998 / Revised version: 29 June 1998 相似文献
12.
We discuss a technique for trying to find all rational points on curves of the form Y
2=f
3
X
6+f
2
X
4+f
1
X
2+f
0, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or
1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this
case, we shall derive an associated family of elliptic curves, defined over a number field ℚα. If each of these elliptic
curves has rank less than the degree of ℚα :
ℚ, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over ℚα) on the elliptic curves, for which x∈ℚ. This in turn allows us to find all ℚ-rational points on the original genus 2 curve. We apply this to give a solution to
a problem of Diophantus (where the sextic in X is irreducible over ℚ), which simplifies the recent solution of Wetherell. We also present two examples where the sextic
in X is reducible over ℚ.
Received: 27 November 1998 / Revised version: 4 June 1999 相似文献
13.
Rémi Léandre 《Probability Theory and Related Fields》2001,120(2):168-182
We define a stochastic cohomology theory related to a stochastic diffeology for the Hoelder loop space. We show that the
stochastic de Rham cohomology groups are equal to the deterministic de Rham cohomology groups of the Hoelder loop space. As
an application, we show that a stochastic line bundle over the Brownian bridge (with fiber almost surely defined) is isomorphic
to a true line bundle over the Hoelder loop space.
Received: 9 November 1998 / Revised version: 14 July 2000 / Published online: 26 April 2001 相似文献
14.
Wolfgang M. Ruppert 《manuscripta mathematica》1998,96(1):17-22
If K is a number field of degree n over Q with discriminant D
K
and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are
infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d
2 such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real
number field of prime degree n then one can find an integral generator α with .
Received: 10 January 1997 / Revised version: 13 January 1998 相似文献
15.
The upper limit and the first gap in the spectrum of genera of -maximal curves are known, see [34], [16], [35]. In this paper we determine the second gap. Both the first and second gaps
are approximately constant times , but this does not hold true for the third gap which is just 1 for while (at most) constant times q for This suggests that the problem of determining the third gap which is the object of current work on -maximal curves could be intricate. Here, we investigate a relevant related problem namely that of characterising those -maximal curves whose genus is equal to the third (or possible the forth) largest value in the spectrum. Our results also
provide some new evidence on -maximal curves in connection with Castelnuovo's genus bound, Halphen's theorem, and extremal curves.
Received: 1 January 2001 / Revised version: 30 July 2001 / Published online: 23 May 2002 相似文献
16.
We study the torsion subgroup of the universal ordinary distribution related to a general number field. We describe a way
to control this subgroup. We apply this method to the special case of an imaginary quadratic field, and we give examples of
such fields where these torsion subgroups are non-trivial.
Received: 4 January 2001 / Revised version: 17 May 2001 相似文献
17.
Sławomir Kołodziej 《Mathematische Zeitschrift》2002,240(4):835-847
It is proved that families of solutions of the complex Monge-Ampère equation with fixed boundary values and certain bounds
on the right hand side are equicontinuous.
Received: 24 April 2001; in final form: 10 August 2001 / Published online: 28 February 2002 相似文献
18.
Guy Henniart 《Mathematische Annalen》2001,319(1):75-87
Résumé. Soit L/K une extension galoisienne finie de corps p-adiques, et soit F un corps de nombres totalement réel, dont le complété en une place v est isomorphe à {\it K}. Si p est impair, nous montrons qu'il existe une extension galoisienne finie E de F, totalement réelle, de même degré que L sur K, et dont le complété en v est isomorphe àL ; quand p vaut 2, nous prouvons une version affaiblie. Ces résultats interviennent dans une preuve des conjectures de Langlands pour
sur les corps p-adiques.
Received March 27, 2000 / Revised May 8, 2000 / Published online December 8, 2000 相似文献
19.
Alexis Michel 《Mathematische Zeitschrift》1999,230(3):451-470
Let E be an elliptic curve with complex multiplication over the ring of integers of an imaginary quadratic field K. Denote by p an odd prime that splits into in and by the unique -extension of K totally ramified above . It is well-known that the Selmer group attached to any finite extension of is analogous to the minus part of the p-class group of divisors of the cyclotomic - extensions of CM number fields. One of the most striking examples of this analogy is the existence of a translation formula à la Kida for the codimension of the Selmer group at the top of the tower. In this article we carry on the analogy with the presentations
of results similar to those proven by Gold and Madan in the cyclotomic case (see [8]), which were the continuation of Kida's
work. More precisely, we describe the -structure of the Selmer group when G is a cyclic group of order p or . In addition, we study the modular representation of G on the subgroup of points of order p of the Selmer group, when G is cyclic of order .
Received December 3, 1997 相似文献