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 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 Nonsolvable number fields ramified only at 3 and 5

2011 ◽  
Vol 147 (3) ◽  
pp. 716-734 ◽  
Author(s):  
Lassina Dembélé ◽  
Matthew Greenberg ◽  
John Voight
Keyword(s):  
Modular Forms ◽  
Number Fields ◽  
Hilbert Modular Forms ◽  
Hilbert Modular

AbstractFor p=3 and p=5, we exhibit a finite nonsolvable extension of ℚ which is ramified only at p, proving in the affirmative a conjecture of Gross. Our construction involves explicit computations with Hilbert modular forms.

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