On the Graded Ring of Siegel Modular Forms of Genus Two

1965 ◽  
Vol 87 (2) ◽  
pp. 502 ◽  
Author(s):  
William F. Hammond
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Graded Ring ◽  
Genus Two

scholarly journals On Siegel modular forms part II

1995 ◽  
Vol 138 ◽  
pp. 179-197 ◽  
Author(s):  
Bernhard Runge
Keyword(s):  
Modular Forms ◽  
Modular Group ◽  
Congruence Subgroup ◽  
Siegel Modular Forms ◽  
Graded Ring

In this paper we compute dimension formulas for rings of Siegel modular forms of genus g = 3. Let denote the main congruence subgroup of level two, the Hecke subgroup of level two and the full modular group. We give the dimension formulas for genus g = 3 for the above mentioned groups and determine the graded ring of modular forms with respect to .

scholarly journals Covariants of binary sextics and vector-valued Siegel modular forms of genus two

2017 ◽  
Vol 369 (3-4) ◽  
pp. 1649-1669 ◽  
Author(s):  
Fabien Cléry ◽  
Carel Faber ◽  
Gerard van der Geer
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two ◽  
Vector Valued

scholarly journals ON THE GRADED RING OF SIEGEL MODULAR FORMS OF DEGREE TWO WITH RESPECT TO A NON-SPLIT SYMPLECTIC GROUP

2012 ◽  
Vol 23 (02) ◽  
pp. 1250032 ◽  
Author(s):  
HIDETAKA KITAYAMA
Keyword(s):  
Modular Forms ◽  
Symplectic Group ◽  
Discrete Subgroup ◽  
Ring Structure ◽  
Siegel Modular Forms ◽  
Graded Ring

We will give an explicit ring structure of the graded ring of Siegel modular forms of degree two with respect to a certain discrete subgroup of Sp(2;ℝ) contained in a non-split ℚ-form. We will also give the fundamental relations among the generators.

On Siegel Modular Forms of Genus Two

1962 ◽  
Vol 84 (1) ◽  
pp. 175 ◽  
Author(s):  
Jun-Ichi Igusa
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two

On Siegel paramodular forms of degree 2 with small levels

2016 ◽  
Vol 27 (02) ◽  
pp. 1650011 ◽  
Author(s):  
Hiroki Aoki
Keyword(s):  
Differential Operator ◽  
Modular Forms ◽  
Siegel Modular Forms ◽  
Graded Ring

In this paper, we show that the graded ring of Siegel paramodular forms of degree [Formula: see text] with level [Formula: see text] has a very simple unified structure, taking with character. All are generated by six modular forms. The first five are obtained by a kind of Maass lift. The last one is obtained by a kind of Rankin–Cohen–Ibukiyama differential operator from the first five. This result is similar to the case of the graded ring of Siegel modular forms of degree [Formula: see text] with respect to [Formula: see text].

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