Quadratic minima and modular forms II

Quadratic Minima and Modular Forms Ii

Carl Ludwig Siegel showed in [Siegel 1969] (English translation, [Siegel 1980]) that the constant terms of certain level one negative-weight modular forms Th are non-vanishing (“ Satz 2 ”), and that this implies an upper bound on the least positive exponent of a non-zero Fourier coefficient for any level one entire modular form of weight h with a non-zero constant term. Level one theta function...

Quadratic Minima and Modular Forms

1991 Mathematics Subject Classi cation: 11F11, 11E20.

Ja n 19 98 QUADRATIC MINIMA AND MODULAR FORMS

We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for Γ0(2). Numerical evidence indicates that a sharper bound holds for the weights h ≡ 2 ( mod 4). We derive upper bounds for the minimum positive integer represented by level two even positive-definite quadratic forms. Our data suggest that, ...

On successive minima of indefinite quadratic forms

m at h . N T ] 1 M ar 1 99 8 QUADRATIC MINIMA AND MODULAR FORMS

We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for Γ0(2). Numerical evidence indicates that a sharper bound holds for the weights h ≡ 2 ( mod 4). We derive upper bounds for the minimum positive integer represented by level two even positive-definite quadratic forms. Our data suggest that, ...