m at h . N T ] 1 M ar 1 99 8 QUADRATIC MINIMA AND MODULAR FORMS
نویسندگان
چکیده
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, for certain meromorphic modular forms and p = 2, 3, the p-order of the constant term is related to the base-p expansion of the order of the pole at infinity.
منابع مشابه
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...
متن کامل1 4 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, ...
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We investigate the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. G(Z) may stand for any of the mapping class, T-duality and U-duality groups Sl(d, Z), SO(d, d, Z) or E d+1(d+1) (Z) respectively. Using G(Z)-invariant mass formulae, we construct invariant modular functions on the symmetric space K\G(...
متن کاملJa 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, ...
متن کامل1 Raising the Levels of Modular Representations
is an irreducible (continuous) representation. We say that ρ is modular of level N , for an integer N ≥ 1, if ρ arises from cusp forms of weight 2 and trivial character on Γo(N). The term “arises from” may be interpreted in several equivalent ways. For our present purposes, it is simplest to work with maximal ideals of the Hecke algebra for weight-2 cusp forms on Γo(N). Namely, let S(N) be the ...
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