On certain zeta functions attached to two Hilbert modular forms: II. The case of automorphic forms on a quaternion algebra

2003 ◽  
pp. 279-317
Author(s):  
Goro Shimura
Keyword(s):  
Modular Forms ◽  
Quaternion Algebra ◽  
Automorphic Forms ◽  
Zeta Functions ◽  
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.

scholarly journals Eichler Maps and Hyperbolic Fourier Expansion

1970 ◽  
Vol 40 ◽  
pp. 173-192 ◽  
Author(s):  
Toyokazu Hiramatsu
Keyword(s):  
Positive Integer ◽  
Modular Forms ◽  
Quadratic Forms ◽  
Fourier Expansion ◽  
Automorphic Forms ◽  
Hilbert Modular Forms ◽  
Ternary Quadratic Forms ◽  
Hilbert Modular ◽  
Lecture Notes

In his lecture notes ([1, pp. 33-35], [2, pp. 145-152]), M. Eichler reduced ‘quadratic’ Hilbert modular forms of dimension —k {k is a positive integer) to holomorphic automorphic forms of dimension — 2k for the reproduced groups of indefinite ternary quadratic forms, by means of so-called Eichler maps.

scholarly journals Mixed Hilbert modular forms and families of abelian varieties

1997 ◽  
Vol 39 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Min Ho Lee
Keyword(s):  
Modular Forms ◽  
Fuchsian Group ◽  
Automorphic Forms ◽  
Elliptic Surface ◽  
Hilbert Modular Forms ◽  
Monodromy Representation ◽  
General Elliptic ◽  
Hilbert Modular ◽  
Upper Half Plane ◽  
Image Position

In [18] Shioda proved that the space of holomorphic 2-forms on a certain type of elliptic surface is canonically isomorphic to the space of modular forms of weight three for the associated Fuchsian group. Later, Hunt and Meyer [6] made an observation that the holomorphic 2-forms on a more general elliptic surface should in fact be identified with mixed automorphic forms associated to an automorphy factor of the formfor z in the Poincaré upper half plane ℋ, g = and χ(g) = , where g is an element of the fundamental group Γ⊂PSL(2, R) of the base space of the elliptic fibration, χ-Γ→SL(2, R) the monodromy representation, and w: ℋ→ℋ the lifting of the period map of the elliptic surface.

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