New Advances in Transcendence Theory

doi:10.1017/CBO9780511897184

This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. Indeed, the evolution of transcendence into a fertile theory with numerous and widespread applications has been one of the most exciting developments of modern mathematics. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles. The work as a whole is an important contribution to mathematics and will be of considerable influence in the further direction of transcendence theory as well as an authoritative account of its current state.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-x
- By A. B.
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Contributors
pp xi-xii
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1 - On effective approximations to cubic irrationals
pp 1-24
- By A. Baker, University of Cambridge, C. L. Stewart, University of Waterloo
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2 - Applications of measure theory and Hausdorff dimension to the theory of Diophantine approximation
pp 25-36
- By V. I. Bernik, Institute of Mathematics
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3 - Galois representations and transcendental numbers
pp 37-55
- By D. Bertrand, Université de Paris
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4 - Some new results on algebraic independence of E-functions
pp 56-67
- By F. Beukers, University of Utrecht
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5 - Algebraic values of hypergeometric functions
pp 68-81
- By F. Beukers, University of Utrecht, J. Wolfart, Goethe Universität
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6 - Some new applications of an inequality of Mason
pp 82-89
- By B. Brindza, Kossuth Lajos University
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7 - Aspects of the Hilbert Nullstellensatz
pp 90-101
- By W. Dale Brownawell, Department of Mathematics
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8 - On the irrationality of certain series: problems and results
pp 102-109
- By P. Erdős, Mathematical Institute
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9 - S-unit equations and their applications
pp 110-174
- By J.-H. Evertse, Department of Pure Mathematics, K. Győry, Kossuth Lajos University, C. L. Stewart, University of Waterloo, R. Tijdeman, University of Leiden
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10 - Decomposable form equations
pp 175-202
- By J.-H. Evertse, Department of Pure Mathematics, K. Győry, Kossuth Lajos University
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11 - On Gelfond's method
pp 203-206
- By N. I. Feldman, University of Moscow
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12 - On effective bounds for certain linear forms
pp 207-214
- By A. I. Galochkin, University of Moscow
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13 - Automata and transcendence
pp 215-228
- By J. H. Loxton, Macquarie University
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14 - The study of Diophantine equations over function fields
pp 229-247
- By R. C. Mason, Caius College, Cambridge, England
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15 - Linear relations on algebraic groups
pp 248-262
- By D. W. Masser, University of Michigan
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16 - Estimates for the number of zeros of certain functions
pp 263-269
- By YU. V. Nesterenko, University of Moscow
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17 - An application of the S-unit theorem to modular forms on Γ0(N)
pp 270-279
- By R. W. K. Odoni, University of Exeter
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18 - Lower bounds for linear forms in logarithms
pp 280-312
- By P. Philippon, Institut Henri Poincaré, M. Waldschmidt, Institut Henri Poincaré
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19 - Reducibility of lacunary polynomials, IX
pp 313-336
- By A. Schinzel, Instytut Matematyczny
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20 - The number of solutions of Thue equations
pp 337-346
- By W. M. Schmidt, University of Colorado
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21 - On arithmetic properties of the values of E-functions
pp 347-351
- By A. B. Shidlovsky, University of Moscow
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22 - Some exponential Diophantine equations
pp 352-365
- By T. N. Shorey, Tata Institute of Fundamental Research
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23 - Arithmetic specializations theory
pp 366-374
- By V. G. Sprindžuk, Institute of Mathematics
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24 - On the transcendence methods of Gelfond and Schneider in several variables
pp 375-398
- By M. Waldschmidt, Institut Henri Poincaré
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25 - A new approach to Baker's theorem on linear forms in logarithms III
pp 399-410
- By G. Wüstholz, Mathematik, ETH-Zentrum
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26 - Linear forms in logarithms in the p-adic case
pp 411-434
- By Kunrui Yu, Institute of Mathematics, Academia Sinica
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New Advances in Transcendence Theory

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