Xem 1-18 trên 18 kết quả Arithmetic progressions
  • We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

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  • Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

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  • 1. Show that there exist in nitely many non similar triangles such that the side-lengths are positive integers and the areas of squares constructed on their sides are in arithmetic progression. 2. Let n be a positive integer. Find the number of those numbers of 2n digits in the binary system for which the sum of digits in the odd places is equal to the sum of digits in the even places.

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:On the Structure of Sets with Few Three-Term Arithmetic Progressions...

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  • We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficiently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we confirm a long standing conjecture of Erd˝s and Folkman on complete sequences. o

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  • Enumerating permutations that avoid three term arithmetic progressions Arun Sharma Department of Mathematics University of California, Berkeley Berkeley, CA 94720 asharma@math.berkeley.edu Submitted: Aug 15, 2008; Accepted: May 4, 2009; Published: May 15, 2009 Mathematics Subject Classifications: 05A15, 05C55. Abstract It is proved that the number of permutations of the set {1, 2, 3, . . . , n} that n avoid three term arithmetic progressions is at most (2.7) for n ≥ 11 and at 21 each end of any such permutation, at least ⌊ n ⌋−6 entries have the same parity. 2 1.

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  • Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: On rainbow arithmetic progressions...

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  • Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Discrepancy of Cartesian Products of Arithmetic Progressions...

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Sets of integers that do not contain long arithmetic progressions...

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Triangle Free Sets and Arithmetic Progressions – Two Pisier Type Problems...

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  • Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Thue-like sequences and rainbow arithmetic progressions Jaroslaw Grytczuk

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  • Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Discrepancy of Sums of Three Arithmetic Progressions...

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  • Chapter 4 LOCAL LIMIT THEOREMS § 1. Formulation of the problem Suppose that the independent, identically distributed random variables X1 , X2 ,. . . . have a lattice distribution with interval h, so that the sum Zn = X1 + X2 + . . . + X„ takes values in the arithmetic progression {na + kh ; k = 0, ± 1, . . . } .

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  • Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

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  • We study the L2 -convergence of two types of ergodic averages. The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg’s proof of Szemer´di’s theorem.

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  • We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. 1. Introduction Arguably the second most famous result of Klaus Roth is his 1953 upper bound [21] on r3 (N ), defined 17 years...

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  • Mathematical theories and methods and effective computational algorithms are crucial in coping with the challenges arising in the sciences and in many areas of their application. New concepts and approaches are necessary in order to overcome the complexity barriers particularly created by nonlinearity, high-dimensionality, multiple scales and uncertainty. Combining advanced mathematical and computational methods and computer technology is an essential key to achieving progress, often even in purely theoretical research.

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  • This is a report on the recent proof of the fundamental lemma. The fundamental lemma and the related transfer conjecture were formulated by R. Langlands in the context of endoscopy theory in [26]. Important arithmetic applications follow from endoscopy theory, including the transfer of automorphic representations from classical groups to linear groups and the construction of Galois representations attached to automorphic forms via Shimura varieties.

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