Abstract
We examine here some new methods borrowed from mathematical physics that are used in analytic number theory and especially in the study of diophantine approximations. Our final product is summarized in a few new results on measures of irrationality of the constants of classical analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Riemann, Oeuvres Mathématiques, Blanchard, Paris, 1968, pp. 353–363.
G. V. Chudnovsky, C. R. Acad. Sci. Paris, 288 (1979) A607–A609.
G. V. Chudnovsky, C. R. Acad. Sci. Paris, 288 (1979) A965–A967.
Ch. Hermite, C. R. Acad. Sci. Paris, 77 (1873) 18–24, 74-79, 226.
G. V. Chudnovsky, Cargese Lectures in Bifurcation Phenomena in Mathematical Physics and Related Topics, D. Reidel, Boston, 1980, 448–510.
G. V. Chudnovsky, J. Math. Pure Appl. 58 (1979) 445–476.
G. Szegö, Orthogonal Polynomials, AMS, Providence, 1938.
K. Alladi, M. L. Robinson, Lecture Notes in Math., Vol. 751, Springer, 1979, 1–9.
G. A. Baker, Jr. Essentials of Padé Approximants, Academic Press, 1975.
G. V. Chudnovsky, Lecture Notes in Physics, Vol. 120, Springer 1980, 103–150.
V. Danilov, Math. Zametki, 24 (1978) No. 4.
A. Y. Khintchine, Continued Fractions, University of Chicago Press, 1964.
K. Mahler, Phil. Trans. Roy. Soc. London, 245A (1953) 371–398.
D. V. Chudnovsky, see this volume.
M. Lüscher, Nuclear Physics B135 (1978) 1.
D. V. Chudnovsky and G. V. Chudnovsky, Lett. Math. Phys. 4 (1980) 373.
D. V. Chudnovsky and G. V. Chudnovsky, J. Math. Pure Appl. (1982), No 1, 1.
D. V. Chudnovsky and G. V. Chudnovsky, Phys. Lett. 82A (1981) 271.
D. V. Chudnovsky and G. V. Chudnovsky, Phys. Lett. 87A (1981) 325.
F. Beukers, Lecture Notes in Math., Vol 888, Springer, 1981, 90.
H. M. Stark, in Applications of Computers in Algebra, Academic Press, 1970, 21.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chudnovsky, G. (1984). Backlund Transformations and Deformations of Linear Differential Equations with Applications to Diophantine Approximations. In: Bars, I., Chodos, A., Tze, CH. (eds) Symmetries in Particle Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5313-1_15
Download citation
DOI: https://doi.org/10.1007/978-1-4899-5313-1_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-5315-5
Online ISBN: 978-1-4899-5313-1
eBook Packages: Springer Book Archive