Andrew M. Odlyzko
Andrew M. Odlyzko has a total of 25 co-authors. Here are the top co-authors by number of shared publications:
- Antoine Joux
École Normale Supérieure
1 shared publication - Arnold Knopfmacher
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
1 shared publication - Boris Pittel
The Ohio State University
1 shared publication - Brian A. LaMacchia
AT&T Bell Laboratories
1 shared publication - Claus Peter Schnorr
FB Math./Inf., Universität Frankfurt, Postfach 111932, Frankfurt a.M., Germany
1 shared publication - D. Stark1 shared publication
Latest Publications
- 1 January 1999
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 8 (2) , 107-118
Jumping Champions
The asymptotic frequency with which pairs of primes below x differ by some fixed integer is understood heuristically, although not rigorously, through the Hardy–Littlewood k-tuple conjecture. Less is known about the differences of consecutive primes. For all x between 1000 and 1012, the most common difference between consecutive primes is 6. We present heuristic and empirical evidence that 6 continues asthe mostcommon difference (jumping champion) up to about x = 1.7427.1035, where it is replaced by 30. In turn, 30 is eventually displaced by 210, which is then displaced by 2310, and so on. Our heuristic arguments are based on a quantitative form of the Hardy–Littlewood conjecture. The technical difficulties in dealing with consecutive primes are formidable enough that even that strong conjecture does not suffice to produce a rigorous proof about the behavior of jumping champions.
- 1 January 1999
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 8 (2) , 107-118
Jumping Champions
The asymptotic frequency with which pairs of primes below x differ by some fixed integer is understood heuristically, although not rigorously, through the Hardy–Littlewood k-tuple conjecture. Less is known about the differences of consecutive primes. For all x between 1000 and 1012, the most common difference between consecutive primes is 6. We present heuristic and empirical evidence that 6 continues asthe mostcommon difference (jumping champion) up to about x = 1.7427.1035, where it is replaced by 30. In turn, 30 is eventually displaced by 210, which is then displaced by 2310, and so on. Our heuristic arguments are based on a quantitative form of the Hardy–Littlewood conjecture. The technical difficulties in dealing with consecutive primes are formidable enough that even that strong conjecture does not suffice to produce a rigorous proof about the behavior of jumping champions.
- 1 November 1998
- Published by Elsevier in Information Processing Letters
- Vol. 68 (4) , 197-199
Attacks on Shamir's ‘RSA for paranoids’
- 1 November 1998
- Published by Elsevier in Information Processing Letters
- Vol. 68 (4) , 197-199
Attacks on Shamir's ‘RSA for paranoids’
- Open Access
- 21 October 1998
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 6 (1) , R2
The Asymptotic Number of Set Partitions with Unequal Block Sizes
The asymptotic behavior of the number of set partitions of an $n$-element set into blocks of distinct sizes is determined. This behavior is more complicated than is typical for set partition problems. Although there is a simple generating function, the usual analytic methods for estimating coefficients fail in the direct approach, and elementary approaches combined with some analytic methods are used to obtain most of the results. Simultaneously, we obtain results on the shape of a random partition of an $n$-element set into blocks of distinct sizes.
- 21 October 1998
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 6 (1) , R2
Open AccessThe Asymptotic Number of Set Partitions with Unequal Block Sizes
The asymptotic behavior of the number of set partitions of an $n$-element set into blocks of distinct sizes is determined. This behavior is more complicated than is typical for set partition problems. Although there is a simple generating function, the usual analytic methods for estimating coefficients fail in the direct approach, and elementary approaches combined with some analytic methods are used to obtain most of the results. Simultaneously, we obtain results on the shape of a random partition of an $n$-element set into blocks of distinct sizes.
- Open Access
- 10 November 1996
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 4 (2) , R14
Monotonic subsequences in dimensions higher than one.
The 1935 result of Erdos and Szekeres that any sequence of at least $n^{2}+1$ real numbers contains a monotonic subsequence of at least $n+1$ terms has stimulated extensive furher research, including a paper of J.B.Kruskal that defined an extension of monotonicity for higher dimensions. This paper provides a proof of a weakened form of Kruskal's conjecture for 2 dimensional Euclidean space by showing that there exists a sequence of n points in the plane for which the longest monotonic subsequences have length $n^{2}+2$ or less.. Weaker results are also obtained for higher dimensions. The average length of the longest increasing monotonic subsequence is shown to be $\sim 2n^{1/2}$ as $n\rightarrow\infty$ for each dimension.- 10 November 1996
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 4 (2) , R14
Open AccessMonotonic subsequences in dimensions higher than one.
The 1935 result of Erdos and Szekeres that any sequence of at least $n^{2}+1$ real numbers contains a monotonic subsequence of at least $n+1$ terms has stimulated extensive furher research, including a paper of J.B.Kruskal that defined an extension of monotonicity for higher dimensions. This paper provides a proof of a weakened form of Kruskal's conjecture for 2 dimensional Euclidean space by showing that there exists a sequence of n points in the plane for which the longest monotonic subsequences have length $n^{2}+2$ or less.. Weaker results are also obtained for higher dimensions. The average length of the longest increasing monotonic subsequence is shown to be $\sim 2n^{1/2}$ as $n\rightarrow\infty$ for each dimension. - 1 November 1996
- Published by American Physical Society (APS) in Physical Review E
- Vol. 54 (5) , R4493-R4495
Gaussian unitary ensemble eigenvalues and Riemannfunction zeros: A nonlinear equation for a new statisticFor infinite Gaussian unitary ensemble random matrices the probability density function for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé equation. Comparison is made with the empirical value of for the zeros of the Riemann function on the critical line, including data from consecutive zeros near zero number .- 1 November 1996
- Published by American Physical Society (APS) in Physical Review E
- Vol. 54 (5) , R4493-R4495
Gaussian unitary ensemble eigenvalues and Riemannfunction zeros: A nonlinear equation for a new statisticFor infinite Gaussian unitary ensemble random matrices the probability density function for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé equation. Comparison is made with the empirical value of for the zeros of the Riemann function on the critical line, including data from consecutive zeros near zero number .- 1 January 1996
- Published by SAGE Publications in Fundamenta Informaticae
- Vol. 28 (3,4) , 297-301
Short Proofs for Nondivisibility of Sparse Polynomials under the Extended Riemann Hypothesis
We prove for the first time an existence of the short (polynomial size) proofs for nondivisibility of two sparse polynomials (putting thus this problem is the class NP) under the Extended Riemann Hypothesis. The divisibility problem is closely relate
- 1 January 1996
- Published by SAGE Publications in Fundamenta Informaticae
- Vol. 28 (3,4) , 297-301
Short Proofs for Nondivisibility of Sparse Polynomials under the Extended Riemann Hypothesis
We prove for the first time an existence of the short (polynomial size) proofs for nondivisibility of two sparse polynomials (putting thus this problem is the class NP) under the Extended Riemann Hypothesis. The divisibility problem is closely relate
- 1 November 1995
- Published by Elsevier in Discrete Mathematics
- Vol. 146 (1-3) , 169-177
Nonabelian sets with distinct k-sums
- 1 November 1995
- Published by Elsevier in Discrete Mathematics
- Vol. 146 (1-3) , 169-177
Nonabelian sets with distinct k-sums
- 1 February 1995
- Published by Taylor & Francis in The American Mathematical Monthly
- Vol. 102 (2) , 113-123
Pebbling a Chessboard
(1995). Pebbling a Chessboard. The American Mathematical Monthly: Vol. 102, No. 2, pp. 113-123.
- 1 February 1995
- Published by Taylor & Francis in The American Mathematical Monthly
- Vol. 102 (2) , 113-123
Pebbling a Chessboard
(1995). Pebbling a Chessboard. The American Mathematical Monthly: Vol. 102, No. 2, pp. 113-123.
- 1 June 1992
- Published by Springer Nature in computational complexity
- Vol. 2 (2) , 111-128
Improved low-density subset sum algorithms
- 1 June 1992
- Published by Springer Nature in computational complexity
- Vol. 2 (2) , 111-128
Improved low-density subset sum algorithms