共查询到20条相似文献,搜索用时 31 毫秒
1.
Mei-Chu Chang 《Geometric And Functional Analysis》2009,19(4):1001-1016
The purpose of the paper is to present new estimates on incomplete character sums in finite fields that are of the strength
of Burgess’ celebrated theorem for prime fields. More precisely, an inequality of this type is obtained in Fp2{F_{p^2}} and also for binary quadratic forms, improving on the work of Davenport–Lewis and on several results due to Burgess. The
arguments are based on new estimates for the multiplicative energy of certain sets that allow us to improve the amplification
step in Burgess’ method. 相似文献
2.
Povilas Banys 《Lithuanian Mathematical Journal》2011,51(3):303-309
In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations
were proved. In this paper, we present the central limit theorem for linear random fields with martingale-differences innovations
satisfying the central limit theorem from [J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields, 110(3):397–426, 1998] and arranged in lexicographical order. 相似文献
3.
Lior Bary-Soroker 《Advances in Mathematics》2012,229(2):854-874
Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove a quantitative arithmetic analog of this conjecture for polynomial rings over pseudo algebraically closed fields. This implies results over large finite fields via model theory. A main tool in the proof is an irreducibility theorem à la Hilbert. 相似文献
4.
We extend a constructive proof of the Eisenbud–Evans–Storch theorem, developed in a previous work by Coquand, Schuster, and Lombardi, from the affine to the projective case. The main tool is that of distributive lattices, which allows us to replace the classical topological arguments by more algebraic and constructive ones. Given a suitable graded ring, we work in the distributive lattice in which the prime filters correspond to the homogeneous prime ideals. The proof presented here is one of the first examples of concrete results obtained using this tool. 相似文献
5.
Jerzy BROWKIN 《数学学报(英文版)》2006,22(1):211-222
The abe-conjecture for the ring of integers states that, for every ε 〉 0 and every triple of relatively prime nonzero integers (a, b, c) satisfying a + b = c, we have max(|a|, |b|, |c|) 〈 rad(abc)^1+ε with a finite number of exceptions. Here the radical rad(m) is the product of all distinct prime factors of m. In the present paper we propose an abe-conjecture for the field of all algebraic numbers. It is based on the definition of the radical (in Section 1) and of the height (in Section 2) of an algebraic number. From this abc-conjecture we deduce some versions of Fermat's last theorem for the field of all algebraic numbers, and we discuss from this point of view known results on solutions of Fermat's equation in fields of small degrees over Q. 相似文献
6.
Nickolai Dobrynin Gerard Duchamp Alexander A. Mikhalev Victor Petrogradsky 《代数通讯》2013,41(11):5275-5302
In this article we consider several aspects of algebraic combinatorics and combinatorial algebra over fields of prime characteristics. P-super-Radford theorem gives the structure of the free associative algebra over a field of prime characteristic with the new multiplication given by the super shuffle product, we show that this algebra is isomorphic to the reduced free super commutative algebra on s-regular words. We prove the elimination theorem for free partially commutative color Lie p-superalgebras and obtain a Schreier type formula for free Lie p-superalgebras using formal power series techniques. 相似文献
7.
In this paper, we give a simpler proof of the Golubchik–Mikhalev–Zelmanov theorem on the structure of isomorphisms between
general linear groups over associative rings, and also prove an extension of this theorem for linear groups over rings graded
by an Abelian group. 相似文献
8.
Maria Karmanova 《Geometric And Functional Analysis》2011,21(6):1358-1374
We develop a new approach to studying the geometry of Carnot–Carathéodory spaces under minimal assumptions on the smoothness
of basis vector fields. We obtain quantitative comparison estimates for the local geometries of two different local Carnot
groups, as well as of a local Carnot group and the original space. As corollaries, we deduce some results that are well-known
and basic for the “smooth” case: the generalized triangle inequality for d
∞, the local approximation theorem for the quasimetric d
∞, the Rashevskiǐ–Chow theorem, the ball-box theorem, and so on. 相似文献
9.
J. Korevaar 《Combinatorica》2001,21(2):239-250
Dedicated to the memory of Paul Erdős
In connection with the elementary proof of the prime number theorem, Erdős obtained a striking quadratic Tauberian theorem
for sequences. Somewhat later, Siegel indicated in a letter how a powerful "fundamental relation" could be used to simplify
the difficult combinatorial proof. Here the author presents his version of the (unpublished) Erdős–Siegel proof. Related Tauberian
results by the author are described.
Received December 20, 1999 相似文献
10.
We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain–Katz–Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid. 相似文献
11.
In this paper, parametric families of Latin squares over Boolean vectors and prime fields constructed earlier are generalized
to the case of Abelian groups. Some criteria for realizability of this construction are presented. Some classification results
are also given.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 3, pp. 65–71, 2006. 相似文献
12.
We prove an equivariant Riemann–Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known
case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in . We then prove and shed some further light on a divisibility result that yields a formula with integral coefficients. Moreover,
we give variants of the main theorem for equivariant locally free sheaves of higher rank. 相似文献
13.
This paper generalizes the Rudin–Carleson theorem for homogeneous solutions of locally solvable real analytic vector fields. 相似文献
14.
Julia Hartmann Anne V. Shepler 《Transactions of the American Mathematical Society》2008,360(1):123-133
Steinberg showed that when a finite reflection group acts on a real or complex vector space of finite dimension, the Jacobian determinant of a set of basic invariants factors into linear forms which define the reflecting hyperplanes. This result generalizes verbatim to fields whose characteristic is prime to the order of the group. Our main theorem gives a generalization of Steinberg's result for groups with a polynomial ring of invariants over arbitrary fields using a ramification formula of Benson and Crawley-Boevey.
15.
A. M. Adamovich 《Mathematical Notes》1997,62(1):8-14
We study the cohomologyG-modules of linear bundles over flag spacesG/B for algebraically closed fields of prime characteristic. Some series of submodules and quotient modules of these modules
are described.
Translated by S. K. Lando
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 10–17, July, 1997. 相似文献
16.
17.
In this paper we extend the coupled contraction mapping theorem proved in partially ordered metric spaces by Gnana Bhaskar
and Lakshmikantham (Nonlinear Anal. TMA 65:1379–1393, 2006) to a coupled coincidence point result for a pair of compatible mappings. A control function has been used in our theorem.
The mappings are assumed to satisfy a weak contractive inequality. Our theorem improves the results of Harjani et al. (Nonlinear
Anal. TMA 74:1749–1760, 2011). The result we have established is illustrated with an example which also shows that the improvement is actual. 相似文献
18.
A. N. Nazarova 《Mathematical Notes》2000,68(3):363-369
The central limit theorem is proved for linear random fields defined on an integer-valued lattice of arbitrary dimension and
taking values in Hilbert space. It is shown that the conditions in the central limit theorem are optimal.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 421–428, September, 2000. 相似文献
19.
主要研究循环数域的导子公式.利用Kronecker-Weber定理及整体域的分歧理论,对于给定除子分歧个数的素数次循环扩域,明确给出了这类数域的导子公式及其个数. 相似文献
20.
We develop and test two novel computational approaches for predicting the mean linear response of a chaotic dynamical system
to small change in external forcing via the fluctuation–dissipation theorem. Unlike the earlier work in developing fluctuation–dissipation
theorem-type computational strategies for chaotic nonlinear systems with forcing and dissipation, the new methods are based
on the theory of Sinai–Ruelle–Bowen probability measures, which commonly describe the equilibrium state of such dynamical
systems. The new methods take into account the fact that the dynamics of chaotic nonlinear forced-dissipative systems often
reside on chaotic fractal attractors, where the classical quasi-Gaussian formula of the fluctuation–dissipation theorem often
fails to produce satisfactory response prediction, especially in dynamical regimes with weak and moderate degrees of chaos.
A simple new low-dimensional chaotic nonlinear forced-dissipative model is used to study the response of both linear and nonlinear
functions to small external forcing in a range of dynamical regimes with an adjustable degree of chaos. We demonstrate that
the two new methods are remarkably superior to the classical fluctuation–dissipation formula with quasi-Gaussian approximation
in weakly and moderately chaotic dynamical regimes, for both linear and nonlinear response functions. One straightforward
algorithm gives excellent results for short-time response while the other algorithm, based on systematic rational approximation,
improves the intermediate and long time response predictions. 相似文献