共查询到20条相似文献,搜索用时 15 毫秒
1.
Liangyi Zhao 《Monatshefte für Mathematik》2007,151(2):165-173
In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish
non-trivial bounds. 相似文献
2.
P. Guerzhoy 《Journal of Number Theory》2007,122(1):151-156
We address a question posed by Ono [Ken Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series, CBMS Reg. Conf. Ser. Math., vol. 102, Amer. Math. Soc., Providence, RI, 2004, Problem 7.30], prove a general result for powers of an arbitrary prime, and provide an explanation for the appearance of higher congruence moduli for certain small primes. One of our results overlaps but does not coincide with a recent result of Jenkins [Paul Jenkins, p-Adic properties for traces of singular moduli, Int. J. Number Theory 1 (1) (2005) 103-107]. This result essentially coincides with a recent result of Edixhoven [Bas Edixhoven, On the p-adic geometry of traces of singular moduli, preprint, 2005, math.NT/0502213 v1], and we hope that the comparison of the methods, which are entirely different, may reveal a connection between the p-adic geometry and the arithmetic of half-integral weight Hecke operators. 相似文献
3.
Stephan Baier 《Advances in Mathematics》2008,219(3):952-985
In this paper, we obtain an unconditional density theorem concerning the low-lying zeros of Hasse-Weil L-functions for a family of elliptic curves. From this together with the Riemann hypothesis for these L-functions, we infer the majorant of 27/14 (which is strictly less than 2) for the average rank of the elliptic curves in the family under consideration. This upper bound for the average rank enables us to deduce that, under the same assumption, a positive proportion of elliptic curves have algebraic ranks equaling their analytic ranks and finite Tate-Shafarevich group. Statements of this flavor were known previously [M.P. Young, Low-lying zeros of families of elliptic curves, J. Amer. Math. Soc. 19 (1) (2005) 205-250] under the additional assumptions of GRH for Dirichlet L-functions and symmetric square L-functions which are removed in the present paper. 相似文献
4.
Ethan Smith 《Journal of Number Theory》2009,129(11):2735-2742
For a fixed number field K, we consider the mean square error in estimating the number of primes with norm congruent to a modulo q by the Chebotarëv Density Theorem when averaging over all q?Q and all appropriate a. Using a large sieve inequality, we obtain an upper bound similar to the Barban-Davenport-Halberstam Theorem. 相似文献
5.
G. Tenenbaum 《Journal of Differential Equations》2007,243(1):70-100
We consider the null-controllability problem for the Schrödinger and heat equations with boundary control. We concentrate on short-time, or fast, controls. We improve recent estimates (see [L. Miller, Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time, J. Differential Equations 204 (2004) 202-226; L. Miller, How violent are fast controls for Schrödinger and plate vibrations?, Arch. Ration. Mech. Anal. 172 (2004) 429-456; L. Miller, Controllability cost of conservative systems: Resolvent condition and transmutation, J. Funct. Anal. 218 (2005) 425-444; L. Miller, The control transmutation method and the cost of fast controls, SIAM J. Control Optim. 45 (2006) 762-772]) on the norm of the operator associating to any initial state the minimal norm control driving the system to zero. Our main results concern the Schrödinger and heat equations in one space dimension. They yield new estimates concerning window problems for series of exponentials as described in [T.I. Seidman, The coefficient map for certain exponential sums, Nederl. Akad. Wetensch. Indag. Math. 48 (1986) 463-478] and in [T.I. Seidman, S.A. Avdonin, S.A. Ivanov, The “window problem” for series of complex exponentials, J. Fourier Anal. Appl. 6 (2000) 233-254]. These results are used, following [L. Miller, The control transmutation method and the cost of fast controls, SIAM J. Control Optim. 45 (2006) 762-772], to deal with the case of several space dimensions. 相似文献
6.
Wenhua Zhao 《Journal of Pure and Applied Algebra》2007,210(2):363-382
This paper is the first of a sequence of papers [W. Zhao, Differential operator specializations of noncommutative symmetric functions (submitted for publication). math.CO/0509134; W. Zhao, Noncommutative symmetric functions and the inversion problem (submitted for publication). math.CV/0509135; W. Zhao, A system over the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509136; W. Zhao, systems over differential operator algebras and the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509138. preprint] on the (noncommutative symmetric) systems over differential operator algebras in commutative or noncommutative variables [W. Zhao, Differential operator specializations of noncommutative symmetric functions (submitted for publication). math.CO/0509134]; the systems over the Grossman-Larson Hopf algebras [R. Grossman, R.G. Larson, Hopf-algebraic structure of families of trees, J. Algebra 126 (1) (1989) 184-210. [MR1023294]; L. Foissy, Les algèbres de Hopf des arbres enracinés décorés I, II, Bull. Sci. Math. 126 (3) (2002) 193-239; (4) 249-288. See also math.QA/0105212. [MR1909461]] of labeled rooted trees [W. Zhao, A system over the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509136]; as well as their connections and applications to the inversion problem [H. Bass, E. Connell, D. Wright, The Jacobian conjecture, reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. 7 (1982) 287-330. [MR 83k:14028]; A. van den Essen, Polynomial automorphisms and the Jacobian conjecture, in: Progress in Mathematics, vol. 190, Birkhäuser Verlag, Basel, 2000. [MR1790619]] and specializations of NCSFs [W. Zhao, Noncommutative symmetric functions and the inversion problem (submitted for publication). math.CV/0509135; W. Zhao, systems over differential operator algebras and the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509138. preprint]. In this paper, inspired by the seminal work [I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V.S. Retakh, J.-Y. Thibon, Noncommutative symmetric functions, Adv. Math. 112 (2) (1995) 218-348. See also hep-th/9407124. [MR1327096]] on NCSFs (noncommutative symmetric functions), we first formulate the notion of systems over associative Q-algebras. We then prove some results for systems in general; the systems over bialgebras or Hopf algebras; and the universal system formed by the generating functions of certain NCSFs in [I.M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V.S. Retakh, J.-Y. Thibon, Noncommutative symmetric functions, Adv. Math. 112 (2) (1995) 218-348. See also hep-th/9407124. [MR1327096]]. Finally, we review some of the main results that will be proved in the following papers [W. Zhao, Differential operator specializations of noncommutative symmetric functions (submitted for publication). math.CO/0509134; W. Zhao, A system over the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509136; W. Zhao, systems over differential operator algebras and the Grossman-Larson Hopf algebra of labeled rooted trees (submitted for publication). math.CO/0509138. preprint] as some supporting examples for the general discussions given in this paper. 相似文献
7.
In this paper we will apply Biró's method in [A. Biró, Yokoi's conjecture, Acta Arith. 106 (2003) 85-104; A. Biró, Chowla's conjecture, Acta Arith. 107 (2003) 179-194] to class number 2 problem of real quadratic fields of Richaud-Degert type and will show that there are exactly 4 real quadratic fields of the form with class number 2, where n2+1 is a even square free integer. 相似文献
8.
Li-Tao Zhang Ting-Zhu Huang Shao-Hua Cheng 《Journal of Computational and Applied Mathematics》2012,236(7):1841-1850
Recently, Wu et al. [S.-L. Wu, T.-Z. Huang, X.-L. Zhao, A modified SSOR iterative method for augmented systems, J. Comput. Appl. Math. 228 (1) (2009) 424-433] introduced a modified SSOR (MSSOR) method for augmented systems. In this paper, we establish a generalized MSSOR (GMSSOR) method for solving the large sparse augmented systems of linear equations, which is the extension of the MSSOR method. Furthermore, the convergence of the GMSSOR method for augmented systems is analyzed and numerical experiments are carried out, which show that the GMSSOR method with appropriate parameters has a faster convergence rate than the MSSOR method with optimal parameters. 相似文献
9.
Jürgen G. Hinz 《Monatshefte für Mathematik》1985,100(4):259-275
Generalizing a method introduced by Elliott in the rational case to number fields in an appropriate way, asymptotic estimates are given for the number of algebraic primes in certain parallelotopes which are primitive roots for almost all (in a certain sense) prime ideal moduli. The proofs depend upon a fundamental lemma of Selberg's rational sieve method and make use of the large sieve in the setting of an algebraic number field. 相似文献
10.
Guangshi Lü 《Journal of Number Theory》2009,129(2):477-487
In this paper we study additive functions on arithmetic progressions with large moduli. We are able to improve some former results given by Elliott. 相似文献
11.
We study the distribution of the size of the Selmer groups arising from a 2-isogeny and its dual 2-isogeny for quadratic twists of elliptic curves with full 2-torsion points in Q. We show that one of these Selmer groups is almost always bounded, while the 2-rank of the other follows a Gaussian distribution. This provides us with a small Tate-Shafarevich group and a large Tate-Shafarevich group. When combined with a result obtained by Yu [G. Yu, On the quadratic twists of a family of elliptic curves, Mathematika 52 (1-2) (2005) 139-154 (2006)], this shows that the mean value of the 2-rank of the large Tate-Shafarevich group for square-free positive integers n less than X is , as X→∞. 相似文献
12.
For a prime p, we consider some natural classes of matrices over a finite field Fp of p elements, such as matrices of given rank or with characteristic polynomial having irreducible divisors of prescribed degrees. We demonstrate two different techniques which allow us to show that the number of such matrices in each of these classes and also with components in a given subinterval [-H, H] [-(p - 1)/2, (p - 1)/2] is asymptotically close to the expected value. 相似文献
13.
In this paper we prove the best possible upper bounds for the number of elements in a set of polynomials with integer coefficients all having the same degree, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. Moreover, we prove that there does not exist a set of more than 12 polynomials with integer coefficients and with the property from above. This significantly improves a recent result of the first two authors with Tichy [A. Dujella, C. Fuchs, R.F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002) 21-33]. 相似文献
14.
Ligia L. Cristea Josef Dick Gunther Leobacher Friedrich Pillichshammer 《Numerische Mathematik》2007,105(3):413-455
In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives
are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m,s)-nets over which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the
root mean square worst-case error converges with order for any ɛ > 0, where 2
m
is the number of points. A similar result for lattice rules has previously been shown by Hickernell.
Ligia L. Cristea is supported by the Austrian Research Fund (FWF), Project P 17022-N 12 and Project S 9609.
Josef Dick is supported by the Australian Research Council under its Center of Excellence Program.
Gunther Leobacher is supported by the Austrian Research Fund (FWF), Project S 8305.
Friedrich Pillichshammer is supported by the Austrian Research Fund (FWF), Project P 17022-N 12, Project S 8305 and Project
S 9609. 相似文献
15.
Claus Bauer 《Frontiers of Mathematics in China》2017,12(2):261-280
We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic progressions. 相似文献
16.
Ling Long 《Journal of Number Theory》2008,128(8):2413-2429
It is now well known that Hecke operators defined classically act trivially on genuine cuspforms for noncongruence subgroups of SL2(Z). Atkin and Swinnerton-Dyer speculated the existence of p-adic Hecke operators so that the Fourier coefficients of their eigenfunctions satisfy three-term congruence recursions. In the previous two papers with the same title ([W.C. Li, L. Long, Z. Yang, On Atkin and Swinnerton-Dyer congruence relations, J. Number Theory 113 (1) (2005) 117-148] by W.C. Li, L. Long, Z. Yang and [A.O.L. Atkin, W.C. Li, L. Long, On Atkin and Swinnerton-Dyer congruence relations (2), Math. Ann. 340 (2) (2008) 335-358] by A.O.L. Atkin, W.C. Li, L. Long), the authors have studied two exceptional spaces of noncongruence cuspforms where almost all p-adic Hecke operators can be diagonalized simultaneously or semi-simultaneously. Moreover, it is shown that the l-adic Scholl representations attached to these spaces are modular in the sense that they are isomorphic, up to semisimplification, to the l-adic representations arising from classical automorphic forms.In this paper, we study an infinite family of spaces of noncongruence cuspforms (which includes the cases in [W.C. Li, L. Long, Z. Yang, On Atkin and Swinnerton-Dyer congruence relations, J. Number Theory 113 (1) (2005) 117-148; A.O.L. Atkin, W.C. Li, L. Long, On Atkin and Swinnerton-Dyer congruence relations (2), Math. Ann. 340 (2) (2008) 335-358]) under a general setting. It is shown that for each space in this family there exists a fixed basis so that the Fourier coefficients of each basis element satisfy certain weaker three-term congruence recursions. For a new case in this family, we will exhibit that the attached l-adic Scholl representations are modular and the p-adic Hecke operators can be diagonalized semi-simultaneously. 相似文献
17.
Richard F. Bass Moritz Kassmann 《Transactions of the American Mathematical Society》2005,357(2):837-850
We consider harmonic functions with respect to the operator
Under suitable conditions on we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator is allowed to be anisotropic and of variable order.
Under suitable conditions on we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator is allowed to be anisotropic and of variable order.
18.
We investigate three combinatorial problems considered by Erd?s, Rivat, Sárközy and Schön regarding divisibility properties of sum sets and sets of shifted products of integers in the context of function fields. Our results in this function field setting are better than those previously obtained for subsets of the integers. These improvements depend on a version of the large sieve for sparse sets of moduli developed recently by the first and third-named authors. 相似文献
19.
Glyn Harman 《Journal of Number Theory》2010,130(9):1969-2002
In this paper we continue our study, begun in G. Harman and A.V. Kumchev (2006) [10], of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious oversight in our first paper, but make further progress on the exponential sums estimates needed, together with an embellishment of the previous sieve technique employed. This leads to an improvement in our bounds for the maximal size of the exceptional sets. 相似文献
20.
Frank Thorne 《Journal of Number Theory》2008,128(6):1784-1794
We adapt the Maier matrix method to the polynomial ring Fq[t], and prove analogues of results of Maier [H. Maier, Primes in short intervals, Michigan Math. J. 32 (1985) 221-225] and Shiu [D.K.L. Shiu, Strings of congruent primes, J. London Math. Soc. 61 (2000) 359-373] concerning the distribution of primes in short intervals. 相似文献