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p-adic L functions and trivial zeroes.

B Perrin-Riou1

  • 1Mathématique, Université de Paris-Sud, Bâtiment 425, F-91405 Orsay, France.

Proceedings of the National Academy of Sciences of the United States of America
|October 19, 2001
PubMed
Summary

This lecture presents new findings and hypotheses concerning the p-adic L function values for the symmetric square of elliptic curves, advancing number theory research.

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Area of Science:

  • Number Theory
  • Algebraic Geometry

Background:

  • Elliptic curves are fundamental objects in number theory with rich arithmetic properties.
  • The symmetric square of an elliptic curve is a related mathematical object studied for its own properties.

Purpose of the Study:

  • To announce recent results on the values of the p-adic L function associated with the symmetric square of an elliptic curve.
  • To present conjectures regarding these p-adic L function values.

Main Methods:

  • The study is based on lecture notes, implying a theoretical and analytical approach.
  • Focuses on the properties and values of p-adic L functions.

Main Results:

  • The lecture announces specific results pertaining to the p-adic L function of the symmetric square.
  • New conjectures are proposed based on these results.

Conclusions:

  • The findings contribute to the understanding of p-adic L functions in the context of elliptic curves.
  • The presented conjectures open avenues for future research in arithmetic geometry.

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