Loeffler, David and Zerbes, Sarah Livia (2012) Wach modules and critical slope p-adic L-functions. Journal für die reine und angewandte Mathematik (Crelles Journal) . ISSN 0075-4102 (In Press)

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Abstract

We study Kato and Perrin-Riou's critical slope p-adic L-function attached to an ordinary modular form using the methods of A. Lei, D. Loeffler and S. L. Zerbes, Wach modules and Iwasawa theory for modular forms, Asian J. Math. 14 (2010), 475–528. We show that it may be decomposed as a sum of two bounded measures multiplied by explicit distributions depending only on the local properties of the modular form at p. We use this decomposition to prove results on the zeros of the p-adic L-function, and we show that our results match the behaviour observed in examples calculated by Pollack and Stevens in “Overconvergent modular symbols and p-adic L-functions”, Ann. Sci. Éc. Norm. Supér. (4) 44 (2011), no. 1, 1–42.

Item Type:	Submitted Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher:	Walter de Gruyter GmbH & Co. KG
ISSN:	0075-4102
Date:	March 2012
Identification Number:	10.1515/crelle.2012.012
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/43664

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