Wach modules and critical slope p-adic L-functions

Abstract

We study Kato and Perrin-Riou's critical slope p-adic L-function attached to an ordinary modular form, using the methods of our earlier work with Lei. 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.

19 pages

References in corpus (2)

• Coleman maps and the p-adic regulator
• Elliptic curves with 3-adic Galois representation surjective mod 3 but not mod 9

Cited by in corpus (6)

• Euler systems for Rankin--Selberg convolutions of modular forms
• Coleman maps and the p-adic regulator
• On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions
• On pairs of p-adic L-functions for weight two modular forms
• Dieudonne crystals and Wach modules for p-divisible fgroups
• Eisenstein degeneration of Euler systems