搜索结果: 181-195 共查到“知识库 数论”相关记录551条 . 查询时间(2.263 秒)
On the Mumford-Tate conjecture for 1-motives
Mumford-Tate conjecture Number Theory Algebraic Geometry
2011/9/21
Abstract: We show that the statement analogous to the Mumford-Tate conjecture for abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associat...
Abstract: We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured ...
Some bounds and limits in the theory of Riemann's zeta function
bounds and limits theory of Riemann's zeta function Number Theory
2011/9/21
Abstract: For any real a>0 we determine the supremum of the real \sigma\ such that \zeta(\sigma+it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different.}
...
Abstract: The calculation, by L.\ Euler, of the values at positive even integers of the Riemann zeta function, in terms of powers of $\pi$ and rational numbers, was a watershed event in the history of...
An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments
Elliptic Analogue Cotangent Dirichlet Series Integer Arguments Number Theory
2011/9/20
Abstract: B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformat...
Abstract: The main topic of this contribution is the problem of counting square-free numbers not exceeding $n$. Before this work we were able to do it in time (Comparing to the Big-O notation, Soft-O ...
Average estimate for additive energy in prime field
Average estimate additive energy prime field Number Theory
2011/9/19
Abstract: Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^{\alpha}, |B|=p^{\beta}$. We will prove that for $p\geqslant p_0(\beta)$ one has $$\sum_{b\in B}E_{+}...
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Non-existence of elliptic curves quadratic fields Number Theory
2011/9/19
Abstract: We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields.
The intersection of cyclic Kummer extensions with cyclotomic extensions
cyclic Kummer extensions cyclotomic extensions Number Theory
2011/9/19
Abstract: We study to which extent cyclic Kummer extensions can be contained in a cyclotomic extension. Let K be a field, and consider an extension of K of the form K(z_m, sqrt[n]{a}) where a is in K,...
Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two
Graphs finite fields of characteristic two Number Theory
2011/9/19
Abstract: In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic two. Formulas are given for the length ...
An Algorithm to Generate Square-Free Numbers and to Compute the Moebius Function
Mobius function square-free numbers zeta function Riemann hypothesis
2011/9/19
Abstract: We introduce an algorithm that iteratively produces a sequence of natural numbers k_i and functions b_i. The number k_(i+1) arises as the first point of discontinuity of b_i above k_i. We de...
Values of certain L-series in positive characteristic
L-functions in positive characteristic Drinfeld modular forms function fields of positive characteristic
2011/9/19
Abstract: We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[...
A Random Matrix Model for Elliptic Curve $L$-Functions of Finite Conductor
Elliptic Curves Low Lying Zeros n-Level Statistics Random Matrix Theory Jacobi Ensembles Characteristic Polynomial
2011/9/19
Abstract: We propose a random matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of their critical zeros away from the center of the critical strip was observed b...
Lower bounds for sumsets of multisets in Z_p^2
Lower bounds sumsets of multisets Number Theory
2011/9/19
Abstract: The classical Cauchy-Davenport theorem implies the lower bound n+1 for the number of distinct subsums that can be formed from a sequence of n elements of the cyclic group Z_p (when p is prim...
Cubic Curves, Finite Geometry and Cryptography
Cubic curves group law non-singularity elliptic curve cryptography finite geometries
2011/9/19
Abstract: Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group st...