On modular forms associated with indefinite quadratic forms of signature (2,n?2)

1977 ◽  
Vol 231 (2) ◽  
pp. 97-144 ◽  
Author(s):  
Takayuki Oda
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Indefinite Quadratic

scholarly journals Siegel theta series for indefinite quadratic forms

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
Christina Roehrig
Keyword(s):  
Differential Equation ◽  
Modular Forms ◽  
Quadratic Forms ◽  
Theta Series ◽  
Second Order ◽  
Transformation Behavior ◽  
Modular Transformation ◽  
Indefinite Quadratic

AbstractThe modular transformation behavior of theta series for indefinite quadratic forms is well understood in the case of elliptic modular forms due to Vignéras, who deduced that solving a differential equation of second order serves as a criterion for modularity. In this paper, we will give a generalization of this result to Siegel theta series.

scholarly journals Theta-functions and Hilbert modular forms

1978 ◽  
Vol 69 ◽  
pp. 97-106 ◽  
Author(s):  
Stephen S. Kudla
Keyword(s):  
Theta Function ◽  
Modular Forms ◽  
Quadratic Forms ◽  
Integral Kernel ◽  
Theta Functions ◽  
Cusp Forms ◽  
Hilbert Modular Forms ◽  
Hilbert Modular ◽  
History Of ◽  
Indefinite Quadratic

The purpose of this note is to show how the theta-functions attached to certain indefinite quadratic forms of signature (2, 2) can be used to produce a map from certain spaces of cusp forms of Nebentype to Hilbert modular forms. The possibility of making such a construction was suggested by Niwa [4], and the techniques are the same as his and Shintani’s [6]. The construction of Hilbert modular forms from cusp forms of one variable has been discussed by many people, and I will not attempt to give a history of the subject here. However, the map produced by the theta-function is essentially the same as that of Doi and Naganuma [2], and Zagier [7]. In particular, the integral kernel Ω(τ, z1, z2) of Zagier is essentially the ‘holomorphic part’ of the theta-function.

scholarly journals The Equivalence of Quadratic Forms

1957 ◽  
Vol 9 ◽  
pp. 526-548 ◽  
Author(s):  
G. L. Watson
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic ◽  
Number Of Classes

The main object of this paper is to find the number of classes in a genus of indefinite quadratic forms, with integral coefficients, in k ≥ 4 variables, distinguishing for even k two cases, according as improper equivalence is or is not admitted.

On Some Entire Modular Forms of Weights and for the Congruence Group Γ0(4N)

1996 ◽  
Vol 3 (5) ◽  
pp. 485-500
Author(s):  
G. Lomadze
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Congruence Group ◽  
Positive Integers

Abstract Entire modular forms of weights and for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.

scholarly journals Strongly indefinite quadratic forms and wild algebras

1990 ◽  
Vol 26 (1) ◽  
pp. 341-351
Author(s):  
Nikolaos Marmaridis
Keyword(s):  
Quadratic Forms ◽  
Indefinite Quadratic
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