共查询到20条相似文献,搜索用时 31 毫秒
1.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
2.
We estimate sums of Kloosterman sums for a real quadratic number field F of the type
3.
Shozo Okada 《Journal of Number Theory》2010,130(8):1750-1762
The classical Dedekind sums were found in transformation formulae of η-functions. It is known that these sums have some properties, especially a reciprocity law
4.
Haruo Ishibashi 《Graphs and Combinatorics》1996,12(1):39-54
In a cyclotomic scheme over a finite field, there are some relations between the irreducible modules of the Terwilliger algebra and the Jacobi sums over the field. These relations were investigated in [3]. In this paper, we replace the finite field by a commutative local ring which is called a Galois ring of characteristic 4. Hence we want to find similar relations between the irreducible modules of the Terwilliger algebra and the Jacobi sums over the local ring. Specifically, if we let be a Galois ring of characteristic 4,X a cyclotomic scheme over with classD and the Terwilliger algebra ofX, then we show that most of the irreducible -modules have standard forms; otherwise, certain relations of the Jacobi sums hold. When the classD is three, we can completely determine the irreducible -modules using Jacobi sums. 相似文献
5.
We prove that Lefschetz fibrations admitting a section of square cannot be decomposed as fiber sums. In particular, Lefschetz fibrations on symplectic 4-manifolds found by Donaldson are indecomposable. This observation also shows that symplectic Lefschetz fibrations are not necessarily fiber sums of holomorphic ones.
6.
A. I. Khrabrov 《Journal of Mathematical Sciences》2001,105(5):2485-2494
The distance and generalized volume ratio for sums of normed spaces X and Y are studied. The sums of spaces X Y are understood in the sense of 2. Bibliography: 8 titles. 相似文献
7.
The problem of determining limiting distributions for sums of records has been studied by several authors who have considered
a variety of assumptions sufficient to ensure that sums of records properly normalized will converge to a non-degenerate distribution.
As a parallel to these endeavors, it is of interest to establish conditions under which the sum of Pfeifer records, properly
normalized, converges. Pfeifer records are defined under the assumption that initial observations are i.i.d. with common survival
function and following the (n−1)-th record value the observations are assumed to have survival function ,n=1,2,.... The study of the asymptotic behavior of sums of Pfeifer records constitutes a natural generalization of work on
sums of classical records. The present paper introduces conditions under which the limit distribution of sums of Pfeifer records
is non-degenerate.
相似文献
8.
We make conjectures and give estimates for how large character sums can be as we vary over all characters mod , and as we vary over real, quadratic characters. In particular we show that the largest sums seem to depend on the value of the character at ``smooth numbers'.
9.
A. N. Frolov 《Journal of Mathematical Sciences》2003,118(6):5650-5657
We investigate the almost sure asymptotic behavior of increments of sums of i.i.d. random variables over increasing runs in an associate sequence. The Shepp law, the Erds–Rényi law, and the Csörg–Révéesz law are obtained for increments of sums over increasing runs formed by random variables taking their values in a fixed interval. Bibliography: 17 titles. 相似文献
10.
Dae San Kim 《Monatshefte für Mathematik》1998,126(1):55-71
For a nontrivial additive character and a multiplicative character of the finite field withq elements, the Gauss sums (trg) overgSp(2n,q) and (detg)(trg) overgGSp(2n, q) are considered. We show that it can be expressed as a polynomial inq with coefficients involving powers of Kloosterman sums for the first one and as that with coefficients involving sums of twisted powers of Kloosterman sums for the second one. As a result, we can determine certain generalized Kloosterman sums over nonsingular matrices and generalized Kloosterman sums over nonsingular alternating matrices, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.Supported in part by Basic Science Research Institute program, Ministry of Education of Korea, BSRI 95-1414 and KOSEF Research Grant 95-K3-0101 (RCAA)Dedicated to my father, Chang Hong Kim 相似文献
11.
Richard C. Bradley 《Journal of Theoretical Probability》1996,9(3):659-678
Schmidt(10) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products. 相似文献
12.
Aaron Pixton 《Journal of Number Theory》2009,129(4):806-13
A conjecture of Gao and Leader, recently proved by Sun, states that if is a sequence of length n in a finite abelian group of exponent n, then either some subsequence of X sums to zero or the set of all sums of subsequences of X has cardinality at least 2n−1. This conjecture turns out to be a simple consequence of a theorem of Olson and White; we investigate generalizations that are not implied by this theorem. In particular, we prove the following result: if is a sequence of length n, the terms of which generate a finite abelian group of rank at least 3, then either some subsequence of X sums to zero or the set of all sums of subsequences of X has cardinality at least 4n−5. 相似文献
13.
Asymptotic normality, tightness, and weak convergence of the magnitude-Winsorized sums formed from symmetric i.i.d. random variables are studied via a new approach that first derives self-normalized (studentized) results and then uses these to derive results for constant normalizations. An application of this method to trimmed sums is also discussed to demonstrate its more general applicability as well as to illustrate its use. 相似文献
14.
H.A. Hassan 《Journal of Mathematical Analysis and Applications》2008,339(2):811-827
We use a sampling theorem associated with second-order discrete eigenvalue problems to derive some trigonometric identities extending the results of Byrne and Smith [G.J. Byrne, S.J. Smith, Some integer-valued trigonometric sums, Proc. Edinburg Math. Soc. 40 (1997) 393-401]. We derive both integral and non-integral valued trigonometric sums. We give illustrative examples involving representations of the trigonometric sums and in an integral-valued polynomial in (2n+1) of degree 2m, . 相似文献
15.
We present a general construction of a family of ordinal sums of a sequence of structures and prove an elimination theorem for the class of ordinal sums in an expanded language. From this we deduce the decidability of the class of -ordinal sums of models of a decidable theory T. As an application of this result we prove that the theory of BL-chains is decidable.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived June 9, 2002; accepted in final form June 19, 2003. 相似文献
16.
The positivity of the sine sums
> in (0, ) has been established by G. Brown and D. C. Wilson. In this paper, we sharpen this result by giving a positive functional estimate from below for these sine sums which does not depend on n. The corresponding problem for a more general class of sine sums is also discussed. 相似文献
17.
Omar Hirzallah 《Linear algebra and its applications》2007,424(1):71-82
We prove several singular value inequalities and norm inequalities involving sums and direct sums of Hilbert space operators. It is shown, among other inequalities, that if X and Y are compact operators, then the singular values of are dominated by those of X ⊕ Y. Applications of these inequalities are also given. 相似文献
18.
V. A. Bykovskii 《Journal of Mathematical Sciences》1987,36(1):8-21
For sums of the form, where, and is a weight function, representations are obtained in terms of the spectral characteristics of the automorphic Laplacian for the full modular group. With their help, asymptotic formulas are derived for sums of the type for P, which generalize the formula, obtained earlier by the author.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Maternaticheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 134, pp. 15–33, 1984. 相似文献
19.
The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statuleviius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights. 相似文献
20.
Neil Hindman Imre Leader Dona Strauss 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2017,87(2):275-287
Suppose that we have a finite colouring of \(\mathbb R\). What sumset-type structures can we hope to find in some colour class? One of our aims is to show that there is such a colouring for which no uncountable set has all of its pairwise sums monochromatic. We also show that there is such a colouring such that there is no infinite set X with \(X+X\) (the pairwise sums from X, allowing repetition) monochromatic. These results assume CH. In the other direction, we show that if each colour class is measurable, or each colour class is Baire, then there is an infinite set X (and even an uncountable X, of size the reals) with \(X+X\) monochromatic. We also give versions for all of these results for k-wise sums in place of pairwise sums. 相似文献