Derivative of symmetric square <i>p</i>-adic <i>L</i>-functions via pull-back formula

Rosso, Giovanni

doi:10.1017/cbo9781316106877.020

Cited by 7 publications

(5 citation statements)

References 37 publications

(72 reference statements)

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“…2. Symmetric squares of modular forms having either split multiplicative or good reduction (Rosso 2014). Here the L -invariant coincides with Fontaine-Mazur's L .f /.…”

Section: Extra Zerosmentioning

confidence: 66%

Iwasawa Theory 2012

Bouganis¹,

Venjakob²

2014

Contributions in Mathematical and Computational Sciences

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“…2. Symmetric squares of modular forms having either split multiplicative or good reduction (Rosso 2014). Here the L -invariant coincides with Fontaine-Mazur's L .f /.…”

Section: Extra Zerosmentioning

confidence: 66%

Iwasawa Theory 2012

Bouganis¹,

Venjakob²

2014

Contributions in Mathematical and Computational Sciences

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“…Indeed, generalizing the paper [Ros15a] where the case g = 1 (the symmetric square of a modular form) has been dealt, one can modify the construction of the Eisenstein family; this allows us to define a second p-adic L-function L * p (x). This new p-adic L-function satisfies the following equality of locally analytic functions around f…”

Section: 2] or [Coa91 §6]) It May Happen Thatmentioning

confidence: 99%

Derivative of the standard 𝑝-adic 𝐿-function associated with a Siegel form

Rosso¹

2018

Trans. Amer. Math. Soc.

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In this paper we construct a two variables p-adic L-function for the standard representation associated with a Hida family of parallel weight genus g Siegel forms, using a method previously developed by Böcherer-Schmidt in one variable. When a form of weight g + 1 is Steinberg at p, a trivial zero appears and, using the method of Greenberg-Stevens, we calculate the first derivative of this p-adic L-function and show that it has the form predicted by a conjecture of Greenberg on trivial zeros.

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“…These p-adic L-functions have been constructed in [Hid00b, §5.3.6] when F = Q. A similar construction works over the totally real fields under some conditions [Ros15]. Note that there is no cyclotomic variable in these p-adic L-functions.…”

Section: We Also Have Analogous Relations Over the P-adic Completions Kmentioning

confidence: 99%

Noncommutative Iwasawa theory arising from Hecke algebras

Aribam¹

2016

Preprint

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Let p be an odd prime and f be a nearly ordinary Hilbert modular Hecke eigenform defined over a totally real field F . Let I be an irreducible component of the universal nearly ordinary or locally cyclotomic deformation of the representation of Gal F that is associated to f . We study the deformation rings over a p-adic Lie extension F ∞ that contains the cyclotomic Z p -extension of F . More precisely, we prove a control theorem about these rings. We introduce a category M I H (G), where G = Gal(F ∞ /F ) and H = Gal(F ∞ /F cyc ), which is the category of modules which are torsion with respect to a certain Ore set, which generalizes the Ore set introduced by Venjakob. For Selmer groups which are in this category, we formulate a Main conjecture in the spirit of Noncommutative Iwasawa theory. We then set up a strategy to prove the conjecture by generalizing work of Burns, Kato, Kakde, and Ritter and Weiss. This requires appropriate generalizations of results of Oliver and Taylor, and Oliver on Logarithms of certain K-groups, which we have presented here.

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Derivative of symmetric square p-adic L-functions via pull-back formula

Cited by 7 publications

References 37 publications

Iwasawa Theory 2012

Iwasawa Theory 2012

Derivative of the standard 𝑝-adic 𝐿-function associated with a Siegel form

Noncommutative Iwasawa theory arising from Hecke algebras

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