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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 x^{3} - y^{2} = k, | 173 | California Institute of Technology, |
Francis B Coghlan, Nelson Stephens | The Diophantine Equation x^{3} - y^{2} = k | 199 | Manchester Univ, Oxford Univ |
Oskar Herrmann | A Non-Trivial Solution of the Diophantine Equation 9(x^{2} + 7y^{2})^{2} - 7(u^{2}+ 7v^{2})^{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 | K_{2} 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•2^{n} | Stockholm Univ |
A photograph of the attendees, family members and organisers: