scholarly journals Central values of twisted base change L-functions associated to Hilbert modular forms

2018 ◽  
Vol 191 ◽  
pp. 213-245
Author(s):  
Qinghua Pi
Keyword(s):  
Modular Forms ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Central Values ◽  
Hilbert Modular

scholarly journals THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS

2015 ◽  
Vol 3 ◽  
Author(s):  
XIN WAN
Keyword(s):  
Modular Forms ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Selmer Group ◽  
Hilbert Modular Form ◽  
Main Conjecture ◽  
Hilbert Modular ◽  
Trivial Character ◽  
The One ◽  
Ordinary Reduction

Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local hypotheses. As a consequence, we prove that for a Hilbert modular form of parallel weight, trivial character, and good ordinary reduction at all primes dividing$p$, if the central critical$L$-value is zero then the$p$-adic Selmer group of it has rank at least one. We also prove that one of the local assumptions in the main result of Skinner and Urban can be removed by a base-change trick.

scholarly journals ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS

2013 ◽  
Vol 56 (1) ◽  
pp. 57-63
Author(s):  
CRISTIAN VIRDOL
Keyword(s):  
Finite Order ◽  
Modular Forms ◽  
Number Fields ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Special Values ◽  
Finite Dimensional ◽  
Arbitrary Base ◽  
Hilbert Modular

AbstractIn this paper we generalize some results, obtained by Shimura, on the special values of L-functions of l-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. The generalization is to the case of the special values of L-functions of arbitrary base change to CM-number fields of l-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations.

scholarly journals Nonvanishing of twists of -functions attached to Hilbert modular forms

2014 ◽  
Vol 17 (A) ◽  
pp. 330-348
Author(s):  
Nathan C. Ryan ◽  
Gonzalo Tornaría ◽  
John Voight
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Modular Forms ◽  
Matrix Theory ◽  
Hilbert Modular Forms ◽  
Central Values ◽  
Hilbert Modular

AbstractWe describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and predictions from random matrix theory.

scholarly journals Ramification of the Eigencurve at Classical RM Points

2019 ◽  
Vol 72 (1) ◽  
pp. 57-88
Author(s):  
Adel Betina
Keyword(s):  
Modular Forms ◽  
Quadratic Field ◽  
Galois Representations ◽  
Theta Series ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Deformation Problem ◽  
Ramification Index ◽  
Hilbert Modular ◽  
Real Quadratic

AbstractJ. Bellaïche and M. Dimitrov showed that the $p$-adic eigencurve is smooth but not étale over the weight space at $p$-regular theta series attached to a character of a real quadratic field $F$ in which $p$ splits. In this paper we prove the existence of an isomorphism between the subring fixed by the Atkin–Lehner involution of the completed local ring of the eigencurve at these points and a universal ring representing a pseudo-deformation problem. Additionally, we give a precise criterion for which the ramification index is exactly 2. We finish this paper by proving the smoothness of the nearly ordinary and ordinary Hecke algebras for Hilbert modular forms over $F$ at the overconvergent cuspidal Eisenstein points, being the base change lift for $\text{GL}(2)_{/F}$ of these theta series. Our approach uses deformations and pseudo-deformations of reducible Galois representations.

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