scholarly journals Density results for automorphic forms on Hilbert modular groups

2003 ◽  
Vol 13 (4) ◽  
pp. 681-719 ◽  
Author(s):  
R.W. Bruggeman ◽  
R.J. Miatello ◽  
I. Pacharoni
Keyword(s):  
Automorphic Forms ◽  
Modular Groups ◽  
Hilbert Modular ◽  
Density Results

scholarly journals Density results for automorphic forms on Hilbert modular groups II

2010 ◽  
Vol 362 (07) ◽  
pp. 3841-3881
Author(s):  
Roelof W. Bruggeman ◽  
Roberto J. Miatello
Keyword(s):  
Automorphic Forms ◽  
Modular Groups ◽  
Hilbert Modular ◽  
Density Results

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 Polygons and Hilbert modular groups

1989 ◽  
Vol 41 (4) ◽  
pp. 633-646 ◽  
Author(s):  
Ryoichi Kobayashi ◽  
Keiko Kushibiki ◽  
Isao Naruki
Keyword(s):  
Modular Groups ◽  
Hilbert Modular

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 The large-scale geometry of Hilbert modular groups

1996 ◽  
Vol 44 (3) ◽  
pp. 435-478 ◽  
Author(s):  
Benson Farb ◽  
Richard Schwartz
Keyword(s):  
Large Scale ◽  
Large Scale Geometry ◽  
Modular Groups ◽  
Hilbert Modular

scholarly journals SYMMETRIES FOR BORCHERDS LIFTS ON HILBERT MODULAR GROUPS AND HIRZEBRUCH–ZAGIER DIVISORS

2013 ◽  
Vol 24 (08) ◽  
pp. 1350065 ◽  
Author(s):  
BERNHARD HEIM ◽  
ATSUSHI MURASE
Keyword(s):  
Modular Group ◽  
Quadratic Field ◽  
Hecke Operators ◽  
The Other ◽  
Real Quadratic Field ◽  
Hilbert Modular Group ◽  
Modular Groups ◽  
Hilbert Modular ◽  
The One ◽  
Real Quadratic

We show certain symmetries for Borcherds lifts on the Hilbert modular group over a real quadratic field. We give two different proofs, the one analytic and the other arithmetic. The latter proof yields an explicit description of the action of Hecke operators on Borcherds lifts.

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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