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

Daniel Delbourgo and Thomas Ward
Source: Experiment. Math. Volume 19, Issue 2 (2010), 195-210.

#### 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.

First Page:
Primary Subjects: 11R23
Secondary Subjects: 11G40, 19B28