Special values of anticyclotomic L-functions modulo λ

Hamieh, Alia

doi:10.1007/s00229-014-0696-4

Cited by 9 publications

(16 citation statements)

References 18 publications

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“…± ) in the so-called supersingular case, as is consistent with the descriptions given by [6, Theorem 1.1(2)] and also [3]. Now, here is a list of other errors and corrections:…”

Section: Erratum -Quaternionic P-adic L-functions Of Hilbert Modular supporting

confidence: 84%

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

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2016

Int. J. Number Theory

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“…± ) in the so-called supersingular case, as is consistent with the descriptions given by [6, Theorem 1.1(2)] and also [3]. Now, here is a list of other errors and corrections:…”

Section: Erratum -Quaternionic P-adic L-functions Of Hilbert Modular supporting

confidence: 84%

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

Order

2016

Int. J. Number Theory

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“…As in [FW09], one should be able to use Theorem 1.1 to get estimates on more general averages of L-values, and apply this to subconvexity and equidistribution problems, but we do not address this here. Theorem 1.1 has also been used in very recent works of Hamieh [Ham14] and Van Order [VO], respectively on valuations of Rankin-Selberg L-values in anticyclotomic towers and on constructing p-adic L-functions.…”

Section: Introduction 1global Resultsmentioning

confidence: 99%

Test vectors and central L-values for GL(2)

2017

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We determine local test vectors for Waldspurger functionals for GL 2 , in the case where both the representation of GL 2 and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger's formula relating twisted central L-values of automorphic representations on GL 2 with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results. 1

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“…Remark. A class of Rankin-Selberg anticyclotomic p-adic L-functions for Hilbert modular forms is constructed in [24]. It also satisfies a property analogoues to (6.1) ([24, §6.2]).…”

Section: 2mentioning

confidence: 99%

p-rigidity and Iwasawa μ-invariants

Burungale

Hida

2017

Alg. Number Th.

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Let F be a totally real field with ring of integers O and p be an odd prime unramified in F. Let p be a prime above p. We prove that a mod p Hilbert modular form associated to F is determined by its restriction to the partial Serre-Tate deformation space Gm ⊗ Op (p-rigidity). Let K/F be an imaginary quadratic CM extension such that each prime of F above p splits in K and λ a Hecke character of K. Partly based on p-rigidity, we prove that the µ-invariant of anticyclotomic Katz p-adic L-function of λ equals the µ-invariant of the full anticyclotomic Katz p-adic L-function of λ. An analogue holds for a class of Rankin-Selberg p-adic L-functions. When λ is self-dual with the root number −1, we prove that the µ-invariant of the cyclotomic derivatives of Katz p-adic L-function of λ equals the µ-invariant of the cyclotomic derivatives of Katz p-adic L-function of λ. Based on previous works of authors and Hsieh, we consequently obtain a formula for the µ-invariant of these p-adic L-functions and derivatives, in most of the cases. We also prove a p-version of a conjecture of Gillard, namely the vanishing of the µ-invariant of Katz p-adic L-function of λ.

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Special values of anticyclotomic L-functions modulo λ

Cited by 9 publications

References 18 publications

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

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

Test vectors and central L-values for GL(2)

p-rigidity and Iwasawa μ-invariants

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