TY - JOUR
T1 - Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
AU - Ahlgren, Scott
AU - Andersen, Nickolas
N1 - Funding Information:
The first author was supported by a grant from the Simons Foundation (#208525 to Scott Ahlgren).
Publisher Copyright:
© 2015, The Author(s).
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.
AB - We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.
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U2 - 10.1007/s40993-015-0011-9
DO - 10.1007/s40993-015-0011-9
M3 - Article
AN - SCOPUS:84949518544
SN - 2363-9555
VL - 1
JO - Research in Number Theory
JF - Research in Number Theory
IS - 1
M1 - 10
ER -