Nonvanishing modulo ℓof Fourier coefficients of Jacobi forms
نویسندگان
چکیده
منابع مشابه
Nonvanishing modulo of Fourier Coefficients of Half-integral Weight Modular Forms
1. Introduction. Let k be an integer and N be a positive integer divisible by 4. If is a prime, denote by v a continuation of the usual-adic valuation on Q to a fixed algebraic closure. Let f be a modular form of weight k + 1/2 with respect to 0 (N) and Nebentypus character χ which has integral algebraic Fourier coefficients a(n), and put v (f) = inf n v (a(n)). Suppose that f is a common eigen...
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S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...
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These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
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We use the relationship between Jacobi forms and vector-valued modular forms to study the Fourier expansions of Jacobi forms of indexes p, p2, and pq for distinct odd primes p, q. Specifically, we show that for such indexes, a Jacobi form is uniquely determined by one of the associated components of the vector-valued modular form. However, in the case of indexes of the form pq or p2, there are ...
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In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2016
ISSN: 2363-9555
DOI: 10.1007/s40993-015-0035-1