共查询到20条相似文献,搜索用时 15 毫秒
1.
Satoshi Kondo 《Journal of Number Theory》2004,104(2):373-377
We define Eisenstein series and theta functions for Drinfeld modules of arbitrary rank, and prove an analog of Kronecker limit formula. 相似文献
2.
Florian Breuer 《Journal of Number Theory》2010,130(5):1241-1250
We derive upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L:K]. Our main tool is the adelic openness of the image of Galois representations, due to Serre, Pink and Rütsche. Our approach is to prove a general result for certain Galois modules, which applies simultaneously to elliptic curves and to Drinfeld modules. 相似文献
3.
Dragos Ghioca 《Journal of Number Theory》2007,125(1):85-94
We study the v-adic distance from the torsion of a Drinfeld module to an affine variety. 相似文献
4.
Let φ be a Drinfeld A-module of arbitrary rank and generic characteristic over a finitely generated field K. If the endomorphism ring of φ over an algebraic closure of K is equal to A, we prove that the image of the adelic Galois representation associated to φ is open. 相似文献
5.
Dragos Ghioca 《Journal of Number Theory》2007,123(2):426-455
We give a lower bound for the local height of a nontorsion element of a Drinfeld module. 相似文献
6.
Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p. 相似文献
7.
So Young Choi 《Journal of Number Theory》2006,119(1):18-27
In this work, we find plane models for certain Drinfeld modular curves X0(n) which have better properties than the plane models derived from the usual Drinfeld modular equations. As an application, we construct ring class fields over imaginary quadratic fields by using singular values of generators of the function field of X0(n). 相似文献
8.
Dragos Ghioca 《Mathematische Annalen》2006,336(4):841-865
We prove an equidistribution result for torsion points of Drinfeld modules of generic characteristic. We also show that similar equidistribution statements would provide proofs for the Manin–Mumford and the Bogomolov conjectures for Drinfeld modules. 相似文献
9.
A. Álvarez 《Journal of Number Theory》2005,110(2):279-316
In a paper from 1994, G.W. Anderson studies the relation between theta functions and rank-one Drinfeld modules. Here, we study generalized theta functions in relation to rank-n Drinfeld modules, explicitly obtaining Plucker coordinates for Drinfeld modules. 相似文献
10.
11.
Gert-Jan van der Heiden 《Monatshefte für Mathematik》2004,143(2):115-143
As is well-known, there exists a Weil pairing for elliptic curves which is a perfect bilinear form from the m-torsion of the elliptic curve E to the m-th roots of unity. In this paper we will show how Andersons paper [1] gives rise to an analogue of this pairing for Drinfeld modules.The author was supported by NWO Grant 613.007.040. The author would like to thank G. Böckle and S. J. Edixhoven for their comments. 相似文献
12.
Helmut Lenzing 《Linear algebra and its applications》2009,430(4):947-956
A polynomial f(T)∈Z[T] is represented by q(T)∈Z[T] if ; f(T) is graphically represented if for χM(T) the characteristic polynomial of a symmetric matrix M. Many instances of Coxeter polynomialsfA(T), for A a finite dimensional algebra, are (graphically) representable. We study the case of extended canonical algebras A, see [H. Lenzing, J.A. de la Peña, Extended canonical algebras and Fuchsian singularities, in press], show that the corresponding polynomials fA(T) are representable and satisfy a Chebysheff type recursion formula. We get consequences for the eigenvalues of the Coxeter transformation of A showing, for instance, that at most four eigenvalues may lie outside the unit circle. 相似文献
13.
Richard Pink 《Journal of Number Theory》2006,116(2):348-372
Let φ be a Drinfeld A-module in special characteristic p0 over a finitely generated field K. For any finite set P of primes p≠p0 of A let ΓP denote the image of Gal(Ksep/K) in its representation on the product of the p-adic Tate modules of φ for all p∈P. We determine ΓP up to commensurability. 相似文献
14.
Richard Pink 《Journal of Number Theory》2006,116(2):324-347
Let ? be a Drinfeld A-module of rank r over a finitely generated field K. Assume that ? has special characteristic p0 and consider any prime p≠p0 of A. If EndKsep(?)=A, we prove that the image of Gal(Ksep/K) in its representation on the p-adic Tate module of ? is Zariski dense in GLr. 相似文献
15.
In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
16.
17.
Let K be a finitely generated field of transcendence degree 1 over a finite field, and set GK?Gal(Ksep/K). Let φ be a Drinfeld A-module over K in special characteristic. Set E?EndK(φ) and let Z be its center. We show that for almost all primes p of A, the image of the group ring Ap[GK] in EndA(Tp(φ)) is the commutant of E. Thus, for almost all p it is a full matrix ring over Z⊗AAp. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p] is absolutely irreducible for almost all p. 相似文献
18.
Let k be a global function field over a finite field and let A be the ring of the elements in k regular outside a fixed place ∞. Let K be a global A-field of finite A-characteristic and let ? be a rank one Drinfeld A-module over K. Given any α∈K, we show that the set of places P of K for which α is a primitive root modulo P under the action of ? possesses a Dirichlet density. We also give conditions for this density to be positive. 相似文献
19.
We construct algebraic curves C defined over a finite prime field such that the number of -rational points of C is large relative to the genus of C. The methods of construction are based on the relationship between algebraic curves and their function fields, as well as
on narrow ray class extensions obtained from Drinfeld modules of rank 1.
Received 21 July 1997; in revised form 5 February 1998 相似文献
20.
Ariel Pacetti 《Journal of Number Theory》2005,113(2):339-379
Let be the negative of a prime, and OK its ring of integers. Let D be a prime ideal in OK of prime norm congruent to . Under these assumptions, there exists Hecke characters ψD of K with conductor (D) and infinite type (1,0). Their L-series L(ψD,s) are associated to a CM elliptic curve A(N,D) defined over the Hilbert class field of K. We will prove a Waldspurger-type formula for L(ψD,s) of the form L(ψD,1)=Ω∑[A],Ir(D,[A],I)m[A],I([D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at |N| and infinity and [A] are class group representatives of K. An application of this formula for the case N=-7 will allow us to prove the non-vanishing of a family of L-series of level 7|D| over K. 相似文献