Experimental Mathematics

The Growth of CM Periods over False Tate Extensions

Daniel Delbourgo and Thomas Ward

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Abstract

We prove weak forms of Kato's ${\rm K}_1$-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use "Magma" to calculate the $\mu$-invariant measuring the discrepancy between the "motivic'' and "automorphic'' {$p$-adic} $L$-functions. Via the two-variable main conjecture, one can then estimate growth in this $\mu$-invariant using arithmetic of the $\Z_p^2$-extension.

Article information

Source
Experiment. Math., Volume 19, Issue 2 (2010), 195-210.

Dates
First available in Project Euclid: 17 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.em/1276784790

Mathematical Reviews number (MathSciNet)
MR2676748

Zentralblatt MATH identifier
1200.11081

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 19B28: $K_1$of group rings and orders [See also 57Q10]

Keywords
Iwasawa theory complex multiplication elliptic cures K-theory $L$-functions

Citation

Delbourgo, Daniel; Ward, Thomas. The Growth of CM Periods over False Tate Extensions. Experiment. Math. 19 (2010), no. 2, 195--210. https://projecteuclid.org/euclid.em/1276784790


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