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On the distribution of spacings between zeros of the zeta function
 MATH. COMP
, 1987
"... A numerical study of the distribution of spacings between zeros of the Riemann zeta function is presented. It is based on values for the first 10 5 zeros and for zeros number 10 12 + 1 to 10 12 + 10 5 that are accurate to within ± 10 − 8, and which were calculated on the Cray1 and Cray XMP compute ..."
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Cited by 121 (9 self)
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A numerical study of the distribution of spacings between zeros of the Riemann zeta function is presented. It is based on values for the first 10 5 zeros and for zeros number 10 12 + 1 to 10 12 + 10 5 that are accurate to within ± 10 − 8, and which were calculated on the Cray1 and Cray XMP computers. This study tests the Montgomery pair correlation conjecture as well as some further conjectures that predict that the zeros of the zeta function behave similarly to eigenvalues of random hermitian matrices. Matrices of this type are used in modeling energy levels in physics, and many statistical properties of their eigenvalues are known. The agreement between actual statistics for zeros of the zeta function and conjectured results is generally good, and improves at larger heights. Several initially unexpected phenomena were found in the data and some were explained by
LOW REDUNDANCY IN STATIC DICTIONARIES WITH CONSTANT QUERY TIME
 SIAM J. COMPUT.
, 2001
"... A static dictionary is a data structure storing subsets of a finite universe U, answering membership queries. We show that on a unit cost RAM with word size Θ(log U), a static dictionary for nelement sets with constant worst case query time can be obtained using B +O(log log U)+o(n) (U) bits ..."
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Cited by 63 (9 self)
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A static dictionary is a data structure storing subsets of a finite universe U, answering membership queries. We show that on a unit cost RAM with word size Θ(log U), a static dictionary for nelement sets with constant worst case query time can be obtained using B +O(log log U)+o(n) (U) bits of storage, where B = ⌈log2 ⌉ is the minimum number of bits needed to represent all nn element subsets of U.
Low Redundancy in Static Dictionaries with O(1) Worst Case Lookup Time
 IN PROCEEDINGS OF THE 26TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP '99
, 1999
"... A static dictionary is a data structure for storing subsets of a nite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size (log jU j), and show that for nelement subsets, constant worst case query time can be obtained us ..."
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Cited by 29 (6 self)
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A static dictionary is a data structure for storing subsets of a nite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size (log jU j), and show that for nelement subsets, constant worst case query time can be obtained using B +O(log log jU j) + o(n) bits of storage, where B = dlog 2 jUj n e is the minimum number of bits needed to represent all such subsets. For jU j = n log O(1) n the dictionary supports constant time rank queries.
Small gaps between prime numbers: the work of GoldstonPintzYıldırım
, 2000
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Low Redundancy in Dictionaries with O(1) Worst Case Lookup Time
 IN PROC. 26TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP
, 1998
"... A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size ze jU j), and show that for nelement subsets, constant worst case query time can be obtain ..."
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Cited by 14 (0 self)
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A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size ze jU j), and show that for nelement subsets, constant worst case query time can be obtained using B +O(log log jU j) + o(n) bits of storage, where B = dlog jU j e is the minimum number of bits needed to represent all such subsets. The solution for dense subsets uses B + O( jU j log log jU j log jU j ) bits of storage, and supports constant time rank queries. In a dynamic setting, allowing insertions and deletions, our techniques give an O(B) bit space usage.
Rectangle Free Coloring of Grids
"... A twodimensional grid is a set Gn,m = [n] × [m]. A grid Gn,m is ccolorable if there is a function χn,m: Gn,m → [c] such that there are no rectangles with all four corners the same color. We address the following question: for which values of n and m is Gn,m ccolorable? This problem can be viewed ..."
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Cited by 10 (3 self)
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A twodimensional grid is a set Gn,m = [n] × [m]. A grid Gn,m is ccolorable if there is a function χn,m: Gn,m → [c] such that there are no rectangles with all four corners the same color. We address the following question: for which values of n and m is Gn,m ccolorable? This problem can be viewed as a bipartite Ramsey problem and is related to a the GallaiWitt theorem (also called the multidimensioanl Van Der Waerden’s Theorem). We determine (1) exactly which grids are 2colorable, (2) exactly which grids are 3colorable, and (3) (assuming a reasonable conjecture) exactly which grids are 4colorable. We use combinatorics, finite fields, and tournament graphs.
On the distribution of imaginary parts of zeros of the Riemann zeta function, II
, 2009
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