scholarly journals On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation

2006 ◽  
pp. 97-102 ◽  
Author(s):  
Masanobu Kaneko
Keyword(s):  
Differential Equation ◽  
Modular Forms

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 ON THE MODULARITY OF SOLUTIONS TO CERTAIN DIFFERENTIAL EQUATIONS OF HYPERGEOMETRIC TYPE

2021 ◽  
pp. 1-7
Author(s):  
HICHAM SABER ◽  
ABDELLAH SEBBAR
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Modular Forms ◽  
Hypergeometric Type

Abstract We answer some questions in a paper by Kaneko and Koike [‘On modular forms arising from a differential equation of hypergeometric type’, Ramanujan J.7(1–3) (2003), 145–164] about the modularity of the solutions of a certain differential equation. In particular, we provide a number-theoretic explanation of why the modularity of the solutions occurs in some cases and does not occur in others. This also proves their conjecture on the completeness of the list of modular solutions after adding some missing cases.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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