## Experimental Mathematics

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

### The Growth of CM Periods over False Tate Extensions

Daniel Delbourgo and Thomas Ward

#### 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