Integral traces of singular values of weak Maass forms
نویسندگان
چکیده
منابع مشابه
Integral Traces of Singular Values of Weak Maass Forms
We define traces associated to a weakly holomorphic modular form f of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a ...
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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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In a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions related to modular forms. Naturally it is of wide interest to find other explicit examples of Maass forms. Here we construct a new infinite family of such forms, arising from overpartitions. As applications we obtain combinatorial decomposit...
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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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In a recent paper, Bruinier and Ono prove that the coefficients of certain weight −1/2 harmonic Maass forms are traces of singular moduli for weak Maass forms. In particular, for the partition function p(n), they prove that p(n) = 1 24n− 1 · ∑ Pp(αQ), where Pp is a weak Maass form and αQ ranges over a finite set of discriminant −24n + 1 CM points. Moreover, they show that 6 · (24n − 1) · Pp(αQ)...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2008
ISSN: 1937-0652
DOI: 10.2140/ant.2008.2.573