共查询到20条相似文献,搜索用时 15 毫秒
1.
Mihran Papikian 《Archiv der Mathematik》2009,92(3):237-250
We prove a genus formula for modular curves of -elliptic sheaves. We use this formula to show that the reductions of modular curves of -elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of tends to infinity.
Received: 14 October 2008
The author was supported in part by NSF grant DMS-0801208 and Humboldt Research Fellowship. 相似文献
2.
Walter Gubler 《manuscripta mathematica》2008,127(4):485-510
We prove equidistribution of a generic net of small points in a projective variety X over a function field K. For an algebraic dynamical system over K, we generalize this equidistribution theorem to a small generic net of subvarieties. For number fields, these results were
proved by Yuan and we transfer here his methods to function fields. If X is a closed subvariety of an abelian variety, then we can describe the equidistribution measure explicitly in terms of convex
geometry. 相似文献
3.
Ernst-Ulrich Gekeler 《manuscripta mathematica》2008,127(1):55-67
We derive formulas for the probabilities of various properties (cyclicity, squarefreeness, generation by random points) of
the point groups of randomly chosen elliptic curves over random prime fields. 相似文献
4.
Ernst Kani 《Archiv der Mathematik》2008,91(3):226-237
Let be the modular curve associated to a congruence subgroup Γ of level N with , and let be its canonical model over . The main aim of this paper is to show that the endomorphism algebra of its Jacobian is generated by the Hecke operators T
p
, with , together with the “degeneracy operators” D
M,d
, D
t
M,d
, for . This uses the fundamental results of Ribet on the structure of together with a basic result on the classification of the irreducible modules of the algebra generated by these operators.
Received: 18 December 2007 相似文献
5.
F. Leprévost M. Pohst A. Schöpp 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2004,74(1):193-203
We describe a way of constructing Jacobians of hyperelliptic curves of genus g ≥ 2, defined over a number field, whose Jacobians
have a rational point of order of some (well chosen) integer l ≥ g + 1; the method is based on a polynomial identity. Using
this approach we construct new families of genus 2 curves defined over — which contain the modular curves X0(31) (and X0(22) as a by-product) and X0(29), the Jacobians of which have a rational point of order 5 and 7 respectively. We also construct a new family of hyperelliptic
genus 3 curves defined over —, which contains the modular curve X0(41), the Jacobians of which have a rational point of order 10. Finally we show that all hyperelliptic modular curves X0(N) with N a prime number fit into the described strategy, except for N = 37 in which case we give another explanation.
The authors thank the FNR (project FNR/04/MA6/11) for their support. 相似文献
6.
It has been known for a long time that the Deligne–Lusztig curves associated to the algebraic groups of type and defined over the finite field all have the maximum number of -rational points allowed by the Weil “explicit formulas”, and that these curves are -maximal curves over infinitely many algebraic extensions of . Serre showed that an -rational curve which is -covered by an -maximal curve is also -maximal. This has posed the problem of the existence of -maximal curves other than the Deligne–Lusztig curves and their -subcovers, see for instance Garcia (On curves with many rational points over finite fields. In: Finite Fields with Applications
to Coding Theory, Cryptography and Related Areas, pp. 152–163. Springer, Berlin, 2002) and Garcia and Stichtenoth (A maximal
curve which is not a Galois subcover of the Hermitan curve. Bull. Braz. Math. Soc. (N.S.) 37, 139–152, 2006). In this paper, a positive answer to this problem is obtained. For every q = n
3 with n = p
r
> 2, p ≥ 2 prime, we give a simple, explicit construction of an -maximal curve that is not -covered by any -maximal Deligne–Lusztig curve. Furthermore, the -automorphism group Aut has size n
3(n
3 + 1)(n
2 − 1)(n
2 − n + 1). Interestingly, has a very large -automorphism group with respect to its genus .
Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni, PRIN 2006–2007. 相似文献
7.
In this note we in the spirit of [1], we give ta structure theorem for a graded ring of modular forms related to the orthogonal group O(2, 5). Our results generalize some results obtained by Klöcker in his Ph.D thesis. 相似文献
8.
In [7], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras
defined over local fields. In this paper, the level and sublevel of composition algebras, of dimension 4 and 8 over rational
function fields over local non-dyadic fields, are determined completely in terms of the local ramification data of the algebras.
The proofs are based on the “classification” of quadratic forms over such fields, as is given in [8].
The first author gratefully acknowledges financial support provided through the European Community’s Human Potential Programme,
under contract HPRN-CT-2002-00287 KTAGS, which made possible an enjoyable stay at Ghent University. 相似文献
9.
We prove the following theorem for a finitely generated field K: Let M be a Galois extension of K which is not separably closed. Then M is not PAC over K.
Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation.
This work constitutes a part of the Ph.D. dissertation of L. Bary-Soroker done at Tel Aviv University under the supervision
of Prof. Dan Haran. 相似文献
10.
Zineb Mimouni René Limage 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):569-574
Within the framework of the study of the fibrillation mechanism in an electrorheological (ER) suspension, this work presents
a comparison between the self similar solutions when the kernel is Ki,j ~ (i−1 + j−1) and the behaviour of the chains growth. Till now, the field induced chains formation has only been studied by numerical
or experimental methods. The work of Fournier and Lauren?ot (Communications in Mathematical Physics 256 2005) on the Smoluchowski’s
equation allows us to present an analytical solution for the field induced pearl chains in a colloidal ER suspension.
René Limage: Chercheur indépendant, dipl?mé de l’Université de Liége. 相似文献
11.
Ekkehard Krätzel 《Archiv der Mathematik》2008,91(6):518-525
The result is: The distribution of values of the enumerating function of finite, non-isomorphic abelian groups in short intervals
is similar to the distribution of square-free numbers in short intervals. Moreover, a new estimate of the error term in the
corresponding asymptotic formula is given, which improves former estimates.
相似文献
12.
Glyn Harman 《Archiv der Mathematik》2008,90(3):239-245
Let P
+(m) denote the greatest prime factor of the positive integer m. Improving and simplifying work of Dartyge [3] we show that
for . Here improves on the previous exponent .
Received: 20 April 2007 相似文献
13.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
14.
The first author introduced an integration theory of vector functions with respect to an operator-valued measure in complete
bornological locally convex vector spaces. In this paper some important results behind this Dobrakov-type integration technique
in non-metrizable spaces are given.
Received: December 10, 2007., Accepted: May 6, 2008. 相似文献
15.
Shunsuke Yamana 《Mathematische Annalen》2009,344(4):853-862
We prove that Siegel modular forms of degree greater than one, integral weight and level N, with respect to a Dirichlet character of conductor are uniquely determined by their Fourier coefficients indexed by matrices whose contents run over all divisors of . The cases of other major types of holomorphic modular forms are included.
The author is supported by the Grant-in-Aid for JSPS fellows. 相似文献
16.
Rogério Serôdio 《Advances in Applied Clifford Algebras》2007,17(2):245-258
We discuss the generalization of results on quaternionic polynomials to the octonionic polynomials. In contrast to the quaternions
the octonionic multiplication is non-associative. This fact although introducing some difficulties nevertheless leads to some
new results. For instance, the monic and non-monic polynomials do not have, in general, the same set of zeros.
Concerning the zeros, it is shown that in the monic and non-monic cases they are not the same, in general, but they belong
to the same set of conjugacy classes.
Despite these difficulties created by the non-associativity, we obtain equivalent results to the quaternionic case with respect
to the number of zeros and the procedure to compute them. 相似文献
17.
For any natural number and any prime (mod 4) not dividing there is a Hermitian modular form of arbitrary genus n over that is congruent to 1 modulo p which is a Hermitian theta series of an OL-lattice of rank p − 1 admitting a fixed point free automorphism of order p. It is shown that also for non-free lattices such theta series are modular forms.
Received: 29 October 2008 相似文献
18.
We calculate the chance that an elliptic curve over a finite field has a specified number of -isogenies which emanate from it. We give a partial answer for abelian varieties of arbitrary dimension.
Received: 20 September 2007 相似文献
19.
Takashi Ichikawa 《Mathematische Annalen》2008,342(3):527-532
Using the moduli theory of abelian varieties and a recent result of Böcherer-Nagaoka on lifting of the generalized Hasse invariant, we show congruences between the weights of Siegel modular forms with congruent Fourier expansions. This result implies that the weights of p-adic Siegel modular forms are well defined. 相似文献