On the -invariant of the cyclotomic derivative of a Katz p -adic -function

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-vani...

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Veröffentlicht in:Journal of the Institute of Mathematics of Jussieu 2015-01, Vol.14 (1), p.131-148
1. Verfasser: Burungale, Ashay A.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748013000388