共查询到20条相似文献,搜索用时 15 毫秒
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The Ramanujan Journal - In the present note, we prove new lower bounds on large values of character sums $$\varDelta (x,q):=\max _{\chi \ne \chi _0} \big \vert \sum _{n\le x} \chi (n)\big \vert $$... 相似文献
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P. E. Frenkel 《Proceedings of the American Mathematical Society》1998,126(11):3199-3200
We give a simple, elementary new proof of a generalization of the following conjecture of Paul Erdos: the sum of the elements of a finite integer set with distinct subset sums is less than 2.
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John B. Friedlander Igor E. Shparlinski 《Proceedings of the American Mathematical Society》2001,129(6):1617-1621
We estimate double exponential sums of the form
where is of multiplicative order modulo the prime and and are arbitrary subsets of the residue ring modulo . In the special case , our bound is nontrivial for with any fixed 0$">, while if in addition we have it is nontrivial for .
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We present common generalizations of some structure results of Freiman, Ruzsa, Balog-Szemerédi and Laczkovich-Ruzsa. We also give some applications to Combinatorial Geometry and Algebra, some of which generalize the aforementioned structure results even further. 相似文献
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Damaraju Raghavarao 《Discrete Mathematics》1974,10(2):401-403
In this note the author applies Boolean sum operation on sets of certain designs to get new series of designs. 相似文献
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A. V. Ostrovsky 《Doklady Mathematics》2007,75(2):213-217
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LetG be a finite abelian group,G?{Z n, Z2?Z2n}. Then every sequenceA={g 1,...,gt} of $t = \frac{{4\left| G \right|}}{3} + 1$ elements fromG contains a subsequenceB?A, |G|=|G| such that $\sum\nolimits_{g_i \in B^{g_i } } { = 0 (in G)} $ . This bound, which is best possible, extends recent results of [1] and [22] concerning the celebrated theorem of Erdös-Ginzburg-Ziv [21]. 相似文献
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A perfect (v,{ki∣1≤i≤s},ρ) difference system of sets (DSS) is a collection of s disjoint ki-subsets Di, 1≤i≤s, of any finite abelian group G of order v such that every non-identity element of G appears exactly ρ times in the multiset {a−b∣a∈Di,b∈Dj,1≤i≠j≤s}. In this paper, we give a necessary and sufficient condition in terms of Jacobi sums for a collection {Di∣1≤i≤s} defined in a finite field Fq of order q=ef+1 to be a perfect (q,{ki∣1≤i≤s},ρ)-DSS, where each Di is a union of cyclotomic cosets of index e (and the zero 0∈Fq). Also, we give numerical results for the cases e=2,3, and 4. 相似文献
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Piotr Zakrzewski 《Topology and its Applications》2008,155(13):1445-1449
We present new characterizations of universally meager sets, shown in [P. Zakrzewski, Universally meager sets, Proc. Amer. Math. Soc. 129 (6) (2001) 1793-1798] to be a category analog of universally null sets. In particular, we address the question of how this class is related to another class of universally meager sets, recently introduced by Todorcevic [S. Todorcevic, Universally meager sets and principles of generic continuity and selection in Banach spaces, Adv. Math. 208 (2007) 274-298]. 相似文献
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Werner Georg Nowak 《Archiv der Mathematik》2012,99(5):433-442
This article is concerned with Ramanujan sums ${c_{\mathcal{I}_1}(\mathcal{I}),}$ where ${\mathcal{I},\mathcal{I}_1}$ are integral ideals in an arbitrary quadratic number field ${\mathbb{Q}(\sqrt{d}).}$ In particular, the asymptotic behavior of sums of ${c_{\mathcal{I}_1}(\mathcal{I}),}$ over both ${\mathcal{I}}$ and ${c_{\mathcal{I}_1}(\mathcal{I}),}$ is investigated. 相似文献
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Rodney G. Downey Michael R. Fellows Venkatesh Raman 《Discrete Applied Mathematics》2000,100(3):155-167
An irredundant set of vertices V′V in a graph G=(V,E) has the property that for every vertex uV′, N[V′−{u}] is a proper subset of N[V′]. We investigate the parameterized complexity of determining whether a graph has an irredundant set of size k, where k is the parameter. The interest of this problem is that while most “k-element vertex set” problems are NP-complete, several are known to be fixed-parameter tractable, and others are hard for various levels of the parameterized complexity hierarchy. Complexity classification of vertex set problems in this framework has proved to be both more interesting and more difficult. We prove that the k-element irredundant set problem is complete for W[1], and thus has the same parameterized complexity as the problem of determining whether a graph has a k-clique. We also show that the “parametric dual” problem of determining whether a graph has an irredundant set of size n−k is fixed-parameter tractable. 相似文献