Computations in non-commutative Iwasawa theory

Details Computations in non-commutative Iwasawa theory Computations in non-commutative Iwasawa theory

2005-09-13

arxiv.org/abs/math/0509286v1

Mathematics

Number Theory

60 pages; with appendix by John Coates and Ramdorai Sujatha

Scientific paper

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension $Q(\mu_p^\infty,\sqrt[p^\infty]{m})/Q$. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.

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