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Proceedings of the London Mathematical Society Advance Access originally published online on November 27, 2006
Proceedings of the London Mathematical Society 2007 94(1):211-272; doi:10.1112/plms/pdl014
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© 2006 London Mathematical Society

Computations in non-commutative Iwasawa theory

T. Dokchitser1, V. Dokchitser1, J. Coates2 and R. Sujatha3

1 Department of Pure Mathematics and Mathematical Statistics
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom
t.dokchitser{at}dpmms.cam.ac.uk
v.dokchitser{at}dpmms.cam.ac.uk
2 Department of Pure Mathematics and Mathematical Statistics
Centre for Mathematical Sciences University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom
J.H.Coates{at}dpmms.cam.ac.uk
3 Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400 005
India
sujatha{at}math.tifr.res.in

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension Formula . 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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