On the quaternionic p-adic L-functions associated to Hilbert modular eigenforms

Details On the quaternionic p-adic L-functions associated to Hilbert modular eigenforms On the quaternionic p-adic L-functions associated to Hilbert modular eigenforms

2011-12-16

arxiv.org/abs/1112.3821v3

International Journal of Number Theory, Vol. 8, No. 4 (2012), 1-35

Mathematics

Number Theory

30 pages, final version

Scientific paper

10.1142/S179304211212500604

We construct p-adic L-functions associated to cuspidal Hilbert modular eigenforms of parallel weight two in certain dihedral or anticyclotomic extensions via the Jacquet-Langlands correspondence, generalizing works of Bertolini-Darmon, Vatsal and others. The construction given here is adelic, which allows us to deduce a precise interpolation formula from a Waldspurger type formula, as well as a formula for the dihedral mu-invariant. We also make a note of Howard's nonvanishing criterion for these p-adic L-functions, which can be used to reduce the associated Iwasawa main conjecture to a certain nontriviality criterion for families of p-adic L-functions.

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