منابع مشابه
Inverse Theorems for Subset Sums
Let A be a nite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to nd lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse problem for subset sums is to determine the structure of the extremal sets A of integers for which jS h ...
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For a set T of integers, let P (T ) be the set of all finite subset sums of T , and let T (x) be the set of all integers of T not exceeding x. Let B = {b1 < b2 < · · · } be a sequence of integers and d1 = 10, d2 = 3b1 + 4, and dn = 3bn−1 + 2 (n ≥ 3). In this paper, we prove that (i) if bn > dn for all n ≥ 1, then there exists a sequence of positive integers A = {a1 < a2 < · · · } such that, for...
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Let > 0. Erdős and Szemerédi conjectured that if A is a set of k positive integers which large k, there must be at least k2−ε integers that can be written as the sum or product of two elements of A. We shall prove this conjecture in the special case that the number of sums is very small. 1 A conjecture of Erdős and Szemerédi Let A be a nonempty, finite set of positive integers, and let |A| deno...
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IAl > ((l/k) + E)n then there is a subset B L A such that 0 < 1 BI 0, let snd(nt) denote the smallest integer that does not divide PI. We prove that for every I-: > 0 there is a constant c = ~(8:) z I, such that for every n > 0 and every rn, n ' +' 6 WI < n'llog'n...
متن کاملLimit Theorems for Theta Sums
For almost all values of x 2 R, the classical theta sum S N (x) = N ?1=2 N X n=1 e 2i n 2 x exhibits an extremely irregular behaviour, as N tends to innnity. This limit is investigated by exploiting a connection to the ergodic properties of ows on the unit tangent bundle of a surface of constant negative curvature.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1995-1273512-1