Wach modules and critical slope p-adic L-functions
2013 ◽
Vol 2013
(679)
◽
pp. 181-206
◽
Keyword(s):
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.
Keyword(s):
Keyword(s):
2012 ◽
Vol 153
(3)
◽
pp. 471-487
◽
Keyword(s):
2010 ◽
Vol 06
(01)
◽
pp. 69-87
◽
Keyword(s):
Keyword(s):
2009 ◽
Vol 05
(05)
◽
pp. 845-857
◽
Keyword(s):
Keyword(s):