New Advances in Transcendence Theory

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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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Editorial Reviews

Attractively produced proceedings of a Symposium on Transcendental Number Theory which took place, under auspices of the London Mathematical Society, at the University of Durham in July, 1986. Contains 26 technical papers. Potential readers appear to be few; among the 50 symposium participants could be found "most of the leading specialists in the field," but that is not to suggest that this is unimportant mathematics, or that it will not at some future date attract more attention than it presently enjoys. The volume certainly merits placement on the shelves of serious mathematical libraries. (NW) Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780521090292
  • Publisher: Cambridge University Press
  • Publication date: 11/20/2008
  • Pages: 448
  • Product dimensions: 5.90 (w) x 8.90 (h) x 1.30 (d)

Table of Contents

Preface; Contributors; 1. On effective approximations to cubic irrationals A. Baker and C. L. Stewart; 2. Applications of measure theory and Haudorff dimension to the theory of Diophantine approximation V. I. Bernik; 3. Galois representations and transcendental numbers D. Bertrand; 4. Some new results on algebraic independance of E-functions F. Beukers; 5. Algebraic values of hypergeometric functions F. Beukers and J. Wolfart; 6. Some new applications of an inequality of Mason B. Brindza; 7. Aspects of the Hilbert Nullstellensatz W. D. Brownawell; 8. On the irrationality of certain series: problems and results P. Erdös; 9. S-unit equations and their applications J.-H. Evertse, K. Györy, C. L. Stewart and R. Tijdeman; 10. Decomposable form equations J.-H. Evertse and K. Györy; 11. On Gelfond's method N. I. Feldman; 12. On effective bounds for certain linear forms A. I. Galochkin; 13. Automata and transcendence J. H. Loxton; 14. The study of Diphantine equations over function fields R. C. Mason; 15. Linear relations on algebraic groups D. W. Masser; 16. Estimates for the number of zeros of certain functions Yu. V. Nesterenko; 17. An applications of the S-unit theorem to modular forms on T0(N) R. W. K. Odoni; 18. Lower bounds for linear forms in logarithms P. Philippon and M. Waldschmidt; 19. Reducibility of lacunary polynomials, IX A. Schinzel; 20. The number of solutions of Thue equations W. M. Schmidt; 21. On arithmetic properties of the values of E-functions A. B. Shidlovsky; 22. Some exponential Deiophantine equations T. N. Shorey; 23. Arithmetic specialisations theory V. G. Sprindžuk; 24. On the transcendence methods of Gelfond and Scheider in several variables M. Waldschmidt; 25. A new approach to Baker's theorem on linear forms in logarithms III G. Wüstholz; 26. Linear forms in logarithms in the p-adic case Kunrui Yu.

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