Zeros on the critical line of Dirichlet series associated with Hilbert modular forms

1982 ◽  
Vol 18 (3) ◽  
pp. 350-373
Author(s):  
V. G. Zhuravlev
Keyword(s):  
Dirichlet Series ◽  
Modular Forms ◽  
Critical Line ◽  
Hilbert Modular Forms ◽  
Hilbert Modular

scholarly journals On the Bloch–Kato conjecture for Hilbert modular forms

2021 ◽  
Author(s):  
Matteo Tamiozzo
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Euler System ◽  
Central Point ◽  
Shimura Curves ◽  
Hilbert Modular Forms ◽  
Reciprocity Laws ◽  
Hilbert Modular ◽  
Special Points

AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

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