共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate the distribution of the numbers x∈[1,p] for which all lie in a subset of the set of multiplicative inverses modulo a prime p. Here the ai are integers coprime to p and the numbers are distinct . 相似文献
2.
3.
4.
V. Suresh 《Journal of Number Theory》2004,107(1):80-94
Let k be a field of characteristic not equal to 2. For n≥1, let denote the nth Galois Cohomology group. The classical Tate's lemma asserts that if k is a number field then given finitely many elements , there exist such that αi=(a)∪(bi), where for any λ∈k∗, (λ) denotes the image of k∗ in . In this paper we prove a higher dimensional analogue of the Tate's lemma. 相似文献
5.
Wendt's determinant of order n is the circulant determinant Wn whose (i,j)-th entry is the binomial coefficient , for 1?i,j?n, where n is a positive integer. We establish some congruence relations satisfied by these rational integers. Thus, if p is a prime number and k a positive integer, then and . If q is another prime, distinct from p, and h any positive integer, then . Furthermore, if p is odd, then . In particular, if p?5, then . Also, if m and n are relatively prime positive integers, then WmWn divides Wmn. 相似文献
6.
H. Kisilevsky 《Journal of Number Theory》2004,104(2):279-286
Suppose that E1 and E2 are elliptic curves over the rational field, , such that for all quadratic fields . We prove that their conductors N(E1), and N(E2) are equal up to squares. If for all quadratic fields , then the same conclusion holds, provided the 2-parts of their Tate-Shafarevich groups are finite. 相似文献
7.
8.
9.
Alex V. Kontorovich 《Journal of Number Theory》2006,117(1):1-13
For every positive integer n, the quantum integer [n]q is the polynomial [n]q=1+q+q2+?+qn-1. A quadratic addition rule for quantum integers consists of sequences of polynomials , , and such that for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials that satisfy the associated functional equation . 相似文献
10.
Najib Ouled Azaiez 《Journal of Number Theory》2008,128(7):1966-1988
We describe the additive structure of the graded ring of quasimodular forms over any discrete and cocompact group Γ⊂PSL(2,R). We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals where I and are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that is contained in some finitely generated ring of meromorphic quasimodular forms with i.e., the same order of growth as 相似文献
11.
M. Godin 《Journal of Number Theory》2003,98(2):320-328
Let k be a number field and Ok its ring of integers. Let Γ be the alternating group A4. Let be a maximal Ok-order in k[Γ] containing Ok[Γ] and its class group. We denote by the set of realizable classes, that is the set of classes such that there exists a Galois extension N/k at most tamely ramified, with Galois group isomorphic to Γ, for which the class of is equal to c, where ON is the ring of integers of N. In this article we determine and we prove that it is a subgroup of provided that k and the 3rd cyclotomic field of are linearly disjoint, and the class number of k is odd. 相似文献
12.
13.
14.
15.
Haseo Ki 《Journal of Number Theory》2008,128(9):2704-2755
16.
Francis Gardeyn 《Journal of Number Theory》2003,100(2):332-362
Let R be a complete discrete valuation -algebra whose residue field is algebraic over , and let K denote its fraction field. In this paper, we study the structure of τ-sheaves M without good reduction on the curve , seen as a rigid analytic space. One motivation is the Tate uniformization theorem for t-motives of Drinfeld modules, which we want to extend to general τ-sheaves. On the other hand, we are interested in the action of inertia on a generic Tate module T?(M) of M.For a given τ-sheaf M on , we prove the existence of a maximal model for M on , an R-model of , and, over a finite separable extension R′ of R, of nondegenerate models for M.We prove the following ‘semistability’ theorem: there exists a finite extension K′ of K, a nonempty open subscheme C′⊂C, and a filtration
17.
Let −D<−4 denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of exists. Let d be a fundamental discriminant prime to D. Let 2k−1 be an odd natural number prime to the class number of . Let χ be the twist of the (2k−1)th power of a canonical Hecke character of by the Kronecker's symbol . It is proved that the vanishing order of the Hecke L-function L(s,χ) at its central point s=k is determined by its root number when , where the constant implied in the symbol ? depends only on k and ?, and is effective for L-functions with root number −1. 相似文献
18.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
19.
Let be a finite field with q=pfelements, where p is a prime number and f is a positive integer. For a nonprincipal multiplicative character χ and a nontrivial additive character ψ on , it is well known that Gauss sum has absolute value . In this paper, we investigate when is a root of unity. 相似文献
20.
Norisato Kataoka 《Journal of Number Theory》2003,101(2):349-375
Let k be a real quadratic number field and the ring of integers and the group of units in k. Denote by the subgroup represented by elements of E of for a prime ideal in k. We show that for a given positive rational integer a, the set of prime numbers p for which the residual index of for lying above p is equal to a has a natural density c under the Generalized Riemann Hypothesis. Moreover, we give the explicit formula of c and conditions to c=0. 相似文献