共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves. 相似文献
2.
Daniel Simson 《Linear algebra and its applications》2010,433(4):699-717
Linear algebra technique in the study of linear representations of finite posets is developed in the paper. A concept of a quadratic wandering on a class of posets I is introduced and finite posets I are studied by means of the four integral bilinear forms (1.1), the associated Coxeter transformations, and the Coxeter polynomials (in connection with bilinear forms of Dynkin diagrams, extended Dynkin diagrams and irreducible root systems are also studied). Bilinear equivalences between some of the forms are established and equivalences with the bilinear forms of Dynkin diagrams and extended Dynkin diagrams are discussed. A homological interpretation of the bilinear forms (1.1) is given and Z-bilinear equivalences between them are discussed. By applying well-known results of Bongartz, Loupias, and Zavadskij-Shkabara, we give several characterisations of posets I, with the Euler form weakly positive (resp. with the reduced Euler form weakly positive), and posets I, with the Tits form weakly positive. 相似文献
3.
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
4.
Mikihito Hirabayashi 《Archiv der Mathematik》2008,90(3):223-229
We give a determinant formula for the relative class number of an imaginary abelian number field, which is a generalization
of Newman’s formula of 1970 and of Skula’s of 1981. By our formula we can determine the signs of these determinants, which
these authors did not give.
Received: 17 May 2007 相似文献
5.
In this paper abelian function fields are restricted to the subfields of cyclotomic function fields. For any abelian function field K/k with conductor an irreducible polynomial over a finite field of odd characteristic, we give a calculating formula of the relative divisor class number of K. And using the given calculating formula we obtain a criterion for checking whether or not the relative divisor class number is divisible by the characteristic of k. 相似文献
6.
Sefi Ladkani 《Linear algebra and its applications》2008,428(4):742-753
We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for triangular algebras, as demonstrated by incidence algebras of posets.We also give a simple, direct proof, that certain products of reflections, defined for any square matrix A with 2 on its main diagonal, and in particular the Coxeter transformation corresponding to a generalized Cartan matrix, can be expressed as , where A+, A- are closely associated with the upper and lower triangular parts of A. 相似文献
7.
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
8.
Nicolae Ciprian Bonciocat 《Journal of Pure and Applied Algebra》2008,212(10):2338-2343
We provide several methods to construct irreducible multivariate polynomials from irreducible polynomials in a smaller number of variables. 相似文献
9.
Artūras Dubickas 《manuscripta mathematica》2007,123(3):353-356
We prove that an algebraic number α is a root of a polynomial with positive rational coefficients if and only if none of its
conjugates is a nonnegative real number. This settles a recent conjecture of Kuba. 相似文献
10.
Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation. 相似文献
11.
Diogo Diniz Claudemir Fidelis Bezerra Júnior 《Journal of Pure and Applied Algebra》2018,222(6):1388-1404
Let F be an infinite field. The primeness property for central polynomials of was established by A. Regev, i.e., if the product of two polynomials in distinct variables is central then each factor is also central. In this paper we consider the analogous property for and determine, within the elementary gradings with commutative neutral component, the ones that satisfy this property, namely the crossed product gradings. Next we consider , where R admits a regular grading, with a grading such that is a homogeneous subalgebra and provide sufficient conditions – satisfied by with the trivial grading – to prove that has the primeness property if does. We also prove that the algebras satisfy this property for ordinary central polynomials. Hence we conclude that, over a field of characteristic zero, every verbally prime algebra has the primeness property. 相似文献
12.
Shabnam Akhtari 《Journal of Number Theory》2008,128(4):884-894
In this article, we study the cyclotomic polynomials of degree N−1 with coefficients restricted to the set {+1,−1}. By a cyclotomic polynomial we mean any monic polynomial with integer coefficients and all roots of modulus 1. By a careful analysis of the effect of Graeffe's root squaring algorithm on cyclotomic polynomials, P. Borwein and K.K. Choi gave a complete characterization of all cyclotomic polynomials with odd coefficients. They also proved that a polynomial p(x) with coefficients ±1 of even degree N−1 is cyclotomic if and only if p(x)=±Φp1(±x)Φp2(±xp1)?Φpr(±xp1p2?pr−1), where N=p1p2?pr and the pi are primes, not necessarily distinct. Here is the pth cyclotomic polynomial. Based on substantial computation, they also conjectured that this characterization also holds for polynomials of odd degree with ±1 coefficients. We consider the conjecture for odd degree here. Using Ramanujan's sums, we solve the problem for some special cases. We prove that the conjecture is true for polynomials of degree α2pβ−1 with odd prime p or separable polynomials of any odd degree. 相似文献
13.
Matthias Bornhofen 《Journal of Number Theory》2009,129(2):247-283
In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian varieties, G. Anderson introduced pure t-motives. In this article we study the arithmetic of the latter. We investigate which pure t-motives are semisimple, that is, isogenous to direct sums of simple ones. We give examples for pure t-motives which are not semisimple. Over finite fields the semisimplicity is equivalent to the semisimplicity of the endomorphism algebra, but also this fails over infinite fields. Still over finite fields we study the Zeta function and the endomorphism rings of pure t-motives and criteria for the existence of isogenies. We obtain answers which are similar to Tate's famous results for abelian varieties. 相似文献
14.
The paper considers bounds on the size of the resultant for univariate and bivariate polynomials. For univariate polynomials we also extend the traditional representation of the resultant by the zeros of the argument polynomials to formal resultants, defined as the determinants of the Sylvester matrix for a pair of polynomials whose actual degree may be lower than their formal degree due to vanishing leading coefficients. For bivariate polynomials, the resultant is a univariate polynomial resulting by the elimination of one of the variables, and our main result is a bound on the largest coefficient of this univariate polynomial. We bring a simple example that shows that our bound is attainable and that a previous sharper bound is not correct. 相似文献
15.
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
16.
17.
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
18.
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
19.
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
20.
《Journal of Number Theory》2003,101(1):32-47
Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials. 相似文献