On Picard Modular Forms

1997 ◽  
Vol 184 (1) ◽  
pp. 259-273 ◽  
Author(s):  
Bernhard Runge
Keyword(s):  
Modular Forms ◽  
Picard Modular Forms

scholarly journals Generators for modules of vector-valued Picard modular forms

2013 ◽  
Vol 212 ◽  
pp. 19-57 ◽  
Author(s):  
Fabien Cléry ◽  
Gerard Van Der Geer
Keyword(s):  
Modular Forms ◽  
Unitary Group ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Picard Modular Forms ◽  
Vector Valued

AbstractWe construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2, 1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.

scholarly journals Generators for modules of vector-valued Picard modular forms

2013 ◽  
Vol 212 ◽  
pp. 19-57
Author(s):  
Fabien Cléry ◽  
Gerard Van Der Geer
Keyword(s):  
Modular Forms ◽  
Unitary Group ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Picard Modular Forms ◽  
Vector Valued

AbstractWe construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2, 1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.

On the Nebentypus of Picard Modular Forms

1988 ◽  
Vol 139 (1) ◽  
pp. 115-137 ◽  
Author(s):  
R.-P. Holzapfel
Keyword(s):  
Modular Forms ◽  
Picard Modular Forms

scholarly journals Degeneration of Hodge structures over Picard modular surfaces

2017 ◽  
Vol 13 (05) ◽  
pp. 1145-1164 ◽  
Author(s):  
Giuseppe Ancona
Keyword(s):  
Modular Forms ◽  
Shimura Varieties ◽  
Manuscripta Math ◽  
Modular Surface ◽  
Hodge Structures ◽  
Picard Modular Forms ◽  
Picard Modular Surfaces

We study variations of Hodge structures over a Picard modular surface, and compute the weights and types of their degenerations through the cusps of the Baily–Borel compactification. These computations are one of the key inputs which allow Wildeshaus [On the interior motive of certain Shimura varieties: the case of Picard surfaces, Manuscripta Math. 148(3) (2015) 351–377] to construct motives associated with Picard modular forms.

scholarly journals An extended Gauss AGM and corresponding Picard modular forms

2008 ◽  
Vol 128 (7) ◽  
pp. 2097-2126 ◽  
Author(s):  
Kenji Koike ◽  
Hironori Shiga
Keyword(s):  
Modular Forms ◽  
Picard Modular Forms

scholarly journals Families of Picard modular forms and an application to the Bloch–Kato conjecture

2019 ◽  
Vol 155 (7) ◽  
pp. 1327-1401
Author(s):  
Valentin Hernandez
Keyword(s):  
Modular Forms ◽  
Three Dimensional ◽  
Positive Sign ◽  
Imaginary Field ◽  
The One ◽  
Picard Modular Forms ◽  
Finite Slope

In this article we construct a p-adic three-dimensional eigenvariety for the group $U$(2,1)($E$), where $E$ is a quadratic imaginary field and $p$ is inert in $E$. The eigenvariety parametrizes Hecke eigensystems on the space of overconvergent, locally analytic, cuspidal Picard modular forms of finite slope. The method generalized the one developed in Andreatta, Iovita and Stevens [$p$-adic families of Siegel modular cuspforms Ann. of Math. (2) 181, (2015), 623–697] by interpolating the coherent automorphic sheaves when the ordinary locus is empty. As an application of this construction, we reprove a particular case of the Bloch–Kato conjecture for some Galois characters of $E$, extending the results of Bellaiche and Chenevier to the case of a positive sign.

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