Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Padé approximations and diophantine geometry.

D V Chudnovsky1, G V Chudnovsky

  • 1Department of Mathematics, Columbia University, New York, NY 10027.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1985
PubMed
Summary

Researchers proved a converse to Eisenstein's theorem using Padé approximations. This advances understanding of algebraic function coefficients and has implications for elliptic curve isogenies.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations.

Proceedings of the National Academy of Sciences of the United States of America·1999
Same author

Classification of hypergeometric identities for pi and other logarithms of algebraic numbers.

Proceedings of the National Academy of Sciences of the United States of America·1998
Same author

The computation of classical constants.

Proceedings of the National Academy of Sciences of the United States of America·1989
Same author

Algebraic complexities and algebraic curves over finite fields.

Proceedings of the National Academy of Sciences of the United States of America·1987
Same author

On applications of diophantine approximations.

Proceedings of the National Academy of Sciences of the United States of America·1984
Same author

On some applications of diophantine approximations.

Proceedings of the National Academy of Sciences of the United States of America·1984

Area of Science:

  • Number Theory
  • Algebraic Geometry
  • Complex Analysis

Background:

  • Eisenstein's theorem addresses the boundedness of denominators for algebraic function coefficients.
  • Understanding these coefficients is crucial in number theory and algebraic geometry.
  • Meromorphic functions provide a framework for parameterizing function classes.

Purpose of the Study:

  • To prove a converse to Eisenstein's theorem for specific function classes.
  • To explore the implications of this converse for the Tate conjecture.
  • To provide an effective description of isogenies for elliptic curves.

Main Methods:

  • Application of Padé approximation techniques.
  • Analysis of functions parametrized by meromorphic functions.
  • Utilizing number-theoretic and algebraic geometry principles.

Main Results:

  • A converse to Eisenstein's theorem is established for the studied function classes.
  • The findings offer new insights into the properties of algebraic function coefficients.
  • The results are directly applicable to the Tate conjecture.

Conclusions:

  • The study successfully extends Eisenstein's theorem using Padé approximations.
  • The work provides a foundation for further research into algebraic functions and elliptic curves.
  • This research contributes to the effective description of isogenies in elliptic curve theory.

Related Experiment Videos