Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
نویسندگان
چکیده
منابع مشابه
Algebraic Formulas for the Coefficients of Half-integral Weight Harmonic Weak Maass Forms
We prove that the coefficients of certain weight −1/2 harmonic Maass forms are “traces” of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vectorvalued harmonic weak Maass forms on Mp2(Z), a result which is of independent interest. We then prove a general theorem which guarantees (...
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Harmonic Maass forms have recently been related to many different topics in number theory: Ramanujan’s mock theta functions, Dyson’s rank generating functions, Borcherds products, and central values and derivatives of quadratic twists of modular L-functions. Motivated by these connections, we obtain exact formulas for the coefficients of harmonic Maass forms of non-positive weight, and we obtai...
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Harmonic weak Maass forms of half-integral weight are the subject of many recent works. They are closely related to Ramanujan’s mock theta functions, their theta lifts give rise to Arakelov Green functions, and their coefficients are often related to central values and derivatives of Hecke L-functions. We present an algorithm to compute harmonic weak Maass forms numerically, based on the automo...
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For integers k ≥ 2, we study two differential operators on harmonic weak Maass forms of weight 2 − k. The operator ξ2−k (resp. D) defines a map to the space of weight k cusp forms (resp. weakly holomorphic modular forms). We leverage these operators to study coefficients of harmonic weak Maass forms. Although generic harmonic weak Maass forms have transcendental coefficients, we show that those...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2013.05.028