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Computers in Number Theory Conference

Oliver Atkin, Bryan John Birch

August 18-23, 1969

The Conference took place in Oxford. Oliver Atkin and Bryan Birch were responsible for supervising the production of the Conference Proceedings. This was the second of a number of Symposia organised by the Laboratory.

The speakers were as follows:

Derrick H Lehmer The Economics of Number Theoretic Computation 1 University of California, Berkeley
Paul T Bateman, J W Brown, R S Hall, Kenneth E Kloss, Rosemarie M Stemmler Linear Relations Connecting the Imaginary Parts of the Zeros of the Zeta Function 11 University of Illinois (2), Syracuse Univ, NBS (2)
H M Stark An Explanation of Some Exotic Continued Fractions Found by Brillhart 21 MIT and Univ of Michigan
Pierre Cartier Some Numerical Computations Relating to Automorphic Functions 37 Univ Strasbourg
Joseph Lehner Automorphic Integrals with Preassigned Period Polynomials and the Eichler Cohomology 49 Univ Maryland and NBS
Morris Newman The Number of Conjugacy Classes of Certain Finite Matrix Groups 57 NBS
Olga Taussky Hilbert's Theorem 94 65 California Institute of Technology,
Andrzej Schinzel Reducibility of Polynomials 73 Mathematics Institute PAN, Warsaw
Albrecht Pfister Sums of Squares in the Function Field !R(x, y) 77 University Mathematical Institute, Mainz
John Leech The Location of Four Squares in an Arithmetic Progression, with some Applications 83 Univ Stirling
Aviezri S Fraenkel Diophantine Equations Involving Generalized Triangular and Tetrahedral Numbers 99 Weizmann Institute of Science and Bar Ilan University, Israel
L J Mordell On the Representation of an Integer as the Sum of Four Integer Cubes 115 Cambridge Univ
R Robert Laxton Arithmetic Properties of Linear Recurrences 119 Univ Nottingham
I Jack Good, R A Gaskins Some Relationships Satisfied by Additive and Multiplicative Recurrent Congruential Sequences, with Implications for Pseudorandom Number Generation 125 Virginia Polytechnic Institute, Hampden-Sydney College, Virginia
David G Cantor Investigation of T-Numbers and E-Sequences 137 UCLA
Joseph B Muskat Use of Computers in Cyclotomy 141 Bar-Ilan University,, Israel
Robert S Spira Calculation of the First Factor of the Cyclotomic Class Number 149 Michigan State Univ, Ann Arbor
Harvey Cohn A Numerical Study of Units in Composite Real Quartic and Octic Fields 153 Univ Arizona
Richard B Lakein Class Numbers and Units of Complex Quartic Fields 167 State University of New York at Buffalo
Marshall Hall, Jr The Diophantine Equation x3 - y2 = k, 173 California Institute of Technology,
Francis B Coghlan, Nelson Stephens The Diophantine Equation x3 - y2 = k 199 Manchester Univ, Oxford Univ
Oskar Herrmann A Non-Trivial Solution of the Diophantine Equation 9(x2 + 7y2)2 - 7(u2+ 7v2)2=2 207 Heidelberg Univ
John Brillhart, James Tonascia and Peter J Weinberger On the Fermat Quotient 213 Univ Arizona, Johns Hopkins Univ, Univ California, Berkeley
J R Smith The Inhomogeneous Minima of Some Totally Real Cubic Fields 223 RNEC, Plymouth,
H J Godwin Computations Relating to Cubic Fields 225 Royal Holloway College,
H Peter F Swinnerton-Dyer The Products of Three and of Four Linear Forms 231 Cambridge Univ
John Larmouth The Enumeration of Perfect Forms 237 Cambridge Univ
Alan M Cohen Two Problems in Diophantine Approximation 241 Univ Wales, Cardiff
Marvin C Wunderlich The Improbable Behaviour of Ulam's Summation Sequence 249 Northern Illinois University
Peter A B Pleasants Non-repetitive Sequences 259 University College, Cardiff
Ronald L Graham On Sorting by Comparisons 263 Bell Labs, Murray Hill
Nicholas Metropolis Spectra of Determinant Values in (0,1) Matrices 271 Los Alamos
Jacobus H van Lint On the Nonexistence of Certain Perfect Codes 277 Technical Univ Eindhoven
Stefan A Burr A Class of Theorems in Additive Number Theory which Lend Themselves to Computer Proof 283 Bell Labs, Whippany
J C P Miller Difference Bases. Three Problems in Additive Number Theory 299 Cambridge Univ
N S Mendelsohn A Natural Generalization of Steiner Triple Systems 323 Univ Manitoba
Ernst S Selmer Doubly Periodic Arrays 339 Univ Bergen
W Fred Lunnon Counting Polyominoes 347 Atlas Computer Laboratory
Alexander M Macbeath Combinatorial Analysis with Values in a Semigroup 373 Univ Birmingham
George E Andrews The Use of Computers in Search of Identities of the Rogers-Ramanujan Type 377 vania State University,
Mohinder S Cheema Computers in the Theory of Partitions 389 Univ Arizona
Robert F Churchhouse Binary Partitions 397 Atlas Computer Laboratory
Donald Burnell, Lorne Houten Multiplanar Partitions 401 Washington State Univ
Paul Erdös Some Problems in Number Theory 405 Academy of Sciences, Budapest,
Richard K Guy Some Unsolved Problems 415 University of Calgary
Pierre Barrucand Languages 423 Univ Manitoba
Author Index 429

Several of the papers presented at the Conference are published elsewhere:

A Oliver L Atkin, and H Peter F Swinnerton-Dyer Modular forms on non-congruence subgroups. In "Proceedings of Symposia in Pure Mathematics, XIII". American Mathematical Society, Providence. ACL and Cambridge Univ
Elwyn R Berlekamp Factoring polynomials over large finite fields Bell Labs
Bryan J Birch K2 of global fields. In "Proceedings of Symposia in Pure Mathematics, XX". American Mathematical Society, Providence. Oxford Univ
Carl-Erik Froberg On the prime zeta function. BIT 8, 187-202. Univ of Washington and Lund Univ
Albrecht Frohlich On the classgroup of integral grouprings of finite abelian groups. Mathematika 16, 143-152. King's College London
Jack Good and Bob Churchhouse (The Riemann hypothesis and pseudorandom features of the Mobius sequence. Math. Comp. 22, 857-862 ACL
Helmut Hasse and Joseph Liang Upper grades K:body for quadratic number field with discriminant. 7, Acta Arithmetica 16, 89-98. Hamburg Univ and Ohio Univ
Hans Riesel Lucasian criteria for the primality of N=h•2n Stockholm Univ

A photograph of the attendees, family members and organisers:

Oxford Number Theory Conference 1969

Oxford Number Theory Conference 1969
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