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On the $\mu $ -invariant of the cyclotomic derivative of a Katz p-adic $L$ -function

Published online by Cambridge University Press:  10 January 2014

Ashay A. Burungale*
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA (ashayburungale@gmail.com)

Abstract

When the branch character has root number $- 1$ , the corresponding anticyclotomic Katz $p$ -adic $L$ -function vanishes identically. For this case, we determine the $\mu $ -invariant of the cyclotomic derivative of the Katz $p$ -adic $L$ -function. The result proves, as an application, the non-vanishing of the anticyclotomic regulator of a self-dual CM modular form with root number $- 1$ . The result also plays a crucial role in the recent work of Hsieh on the Eisenstein ideal approach to a one-sided divisibility of the CM main conjecture.

Type
Research Article
Copyright
©Cambridge University Press 2013 

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References

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On the $\mu $ -invariant of the cyclotomic derivative of a Katz p-adic $L$ -function
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