New Advances in Transcendence Theory

The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.

Alan Baker (Edited by)

9780521090292, Cambridge University Press

Paperback / softback, published 20 November 2008

448 pages
22.9 x 15.2 x 0.3 cm, 0.65 kg

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.

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.

Subject Areas: Number theory [PBH]