共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Lomadze 《Georgian Mathematical Journal》1995,2(5):491-516
A method of finding the so-called Liouville's type formulas for the number of representations of integers by $$a_1 (x_1^2 + x_2^2 ) + a_2 (x_3^2 + x_4^2 ) + a_3 (x_5^2 + x_6^2 ) + a_4 (x_7^2 + x_8^2 ) + a_5 (x_9^2 + x_{10}^2 )$$ quadratic forms is developed. 相似文献
2.
Takashi Agoh 《manuscripta mathematica》1998,95(3):311-321
In this paper we shall mainly study additive representations of integers prime to the first m primes as a sum of some integers having a peculiar property. The conjectures of Goldbach and twin primes are also observed
in connection with these representations of integers.
Received: 20 October 1997 相似文献
3.
Melvyn B. Nathanson 《Israel Journal of Mathematics》1987,57(2):129-136
Lehh ≧ 2, and let ?=(B 1, …,B h ), whereB 1 ? N={1, 2, 3, …} fori=1, …,h. Denote by g?(n) the number of representations ofn in the formn=b 1 …b h , whereb i ∈B i . If v (n) > 0 for alln >n 0, then ? is anasymptotic multiplicative system of order h. The setB is anasymptotic multiplicative basis of order h ifn=b 1 …b n is solvable withb i ∈B for alln >n 0. Denote byg(n) the number of such representations ofn. LetM(h) be the set of all pairs (s, t), wheres=lim g? (n) andt=lim g? (n) for some multiplicative system ? of orderh. It is proved that {fx129-1} In particular, it follows thats ≧ 2 impliest=∞. A corollary is a theorem of Erdös that ifB is a multiplicative basis of orderh ≧ 2, then lim g? g(n)=∞. Similar results are obtained for asymptotic union bases of finite subsets of N and for asymptotic least common multiple bases of integers. 相似文献
4.
Takashi Agoh 《manuscripta mathematica》1998,95(1):311-321
In this paper we shall mainly study additive representations of integers prime to the firstm primes as a sum of some integers having a peculiar property. The conjectures of Goldbach and twin primes are also observed
in connection with these representations of integers. 相似文献
5.
Formulas for the number of primitive representations of any integer n as a sum of k squares are given, for 2 ≤ k ≤ 8, and for certain values of n, for 9 ≤ k ≤ 12. The formulas have a similar structure and are striking for their simplicity.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—11E25; Secondary—05A15, 33E05. 相似文献
6.
E. P. Golubeva 《Journal of Mathematical Sciences》1982,18(3):324-329
Continuing the work in an earlier paper, the author uses an assumption concerning the location of zeros of Dirichlet L-series in order to derive an asymptotic formula for the number of representations of large integers by the ternary form f(x,y,z)=x2+2y2+Dz2, where D is of the form x2+2y2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 53–59, 1978. 相似文献
7.
Shaun Cooper 《Journal of Number Theory》2003,103(2):135-162
Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p,
8.
Let f be an integral homogeneous polynomial of degree d, and
let
be the level set for each
. For a compact
subset in
), set
We define the notion of Hardy-Littlewood system for the sequence {Vm},
according as the asymptotic of
as
coincides
with the one
predicted by Hardy-Littlewood circle method. Using a recent work of Eskin
and Oh [EO], we then show for a large family of invariant polynomialsf,
the level sets {Vm} are Hardy-Littlewood. In particular, our results yield
a new proof of Siegel mass formula for quadratic forms. 相似文献
9.
Applications of signed digit representations of an integer include computer arithmetic, cryptography, and digital signal processing. An integer of length n bits can have several binary signed digit (BSD) representations and their number depends on its value and varies with its length. In this paper, we present an algorithm that calculates the exact number of BSDR of an integer of a certain length. We formulate the integer that has the maximum number of BSDR among all integers of the same length. We also present an algorithm to generate a random BSD representation for an integer starting from the most significant end and its modified version which generates all possible BSDR. We show how the number of BSD representations of k increases as we prepend 0s to its binary representation. 相似文献
10.
A. Sárközy 《Acta Mathematica Hungarica》1981,38(1-4):157-181
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14.
O. M. Fomenko 《Journal of Mathematical Sciences》1988,43(4):2608-2613
Exact formulas are derived for the number of the representations of positive integers by certain positive ternary quadratic forms, belonging to multiclass genera. The Fourier coefficients of the corresponding cusp forms (on the basis of the known results of Waldspurger and Tunnell) are expressed in terms of the values of the Hasse-Weil L-functions of certain elliptic curves at the center of the critical strip.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 154, pp. 154–162, 1986. 相似文献
15.
Janos Galambos 《Journal of Number Theory》1977,9(3):338-341
Let ?(N) > 0 be a function of positive integers N and such that ?(N) → 0 and N?(N) → ∞ as N → + ∞. Let NνN(n:…) be the number of positive integers n ≤ N for which the property stated in the dotted space holds. Finally, let g(n; N, ?, z) be the number of those prime divisors p of n which satisfy NZ?(N) ? p ? N?(N), 0 < z < 1 In the present note we show that for each k = 0, ±1, ±2,…, as N → ∞, limvN(n : g(n; N, ?, z) ? g(n + 1; N, ?z) = k) exists and we determine its actual value. The case k = 0 induced the present investigation. Our solution for this value shows that the natural density of those integers n for which n and n + 1 have the same number of prime divisors in the range (1) exists and it is positive. 相似文献
16.
We study compatible families of four-dimensional Galois representations constructed in the étale cohomology of a smooth projective
variety. We prove a theorem asserting that the images will be generically large if certain conditions are satisfied. We only
consider representations with coefficients in an imaginary quadratic field. We apply our result to an example constructed
by Jasper Scholten (A non-selfdual 4-dimensional Galois representation, , 1999), obtaining a family of linear groups and one of unitary groups as Galois groups over .
Research partially supported by MEC grant MTM2006-04895. 相似文献
17.
We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations) in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple representation of integers that we suitably effectivize in order to develop an associated Kolmogorov theory. Such effectivizations are particular instances of a general notion of “self‐enumerated system” that we introduce in this paper. Our main result asserts that, with such effectivizations, Kolmogorov theory allows to quantitatively distinguish the underlying semantics. We characterize the families obtained by such effectivizations and prove that the associated Kolmogorov complexities constitute a hierarchy which coincides with that of Kolmogorov complexities defined via jump oracles and/or infinite computations (cf. [6]). This contrasts with the well‐known fact that usual Kolmogorov complexity does not depend (up to a constant) on the chosen arithmetic representation of integers, let it be in any base n ≥ 2 or in unary. Also, in a conceptual point of view, our result can be seen as a mean to measure the degree of abstraction of these diverse semantics. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
Binary signed digit representation (BSD-R) of an integer is widely used in computer arithmetic, cryptography and digital signal processing. This paper studies what the exact number of optimal BSD-R of an integer is and how to generate them entirely. We also show which kinds of integers have the maximum number of optimal BSD-Rs. 相似文献
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20.
A. V. Domrin 《Mathematical Notes》1995,57(2):167-170
This research was accomplished with the financial support of the Russian Foundation for Fundamental Research, Grant No. 93-01-00225. 相似文献