Correction and addendum to: “The Fourier expansion of Hecke operators for vector-valued modular forms”. (English) Zbl 1502.11049

Stein, Oliver

Funct. Approximatio, Comment. Math. 67, No. 2, 189-198 (2022).

Summary: We correct a mistake in our paper [ibid. 52, No. 2, 229–252 (2015; Zbl 1398.11073)] leading to erroneous formulas in Theorems 5.2 and 5.4. As an immediate corollary of a formula in [V. Bouchard et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 15, Paper 041, 31 p. (2019; Zbl 1440.11060)] we give a formula which relates the Hecke operators \(T(p^2)\circ T(p^{2l-2})\), \(T(p^{2l})\) and \(T(p^{2l-4})\) and comment on it.

MSC:

11F25	Hecke-Petersson operators, differential operators (one variable)
11F27	Theta series; Weil representation; theta correspondences
11L05	Gauss and Kloosterman sums; generalizations
11E08	Quadratic forms over local rings and fields

Keywords:

Weil representation; vector-valued modular forms; Hecke operators; Fourier expansion

Citations:

Zbl 1398.11073; Zbl 1440.11060

References:

[1]	[BCJ] V. Bouchard, T. Creutzig, A. Joshi, Hecke Operators on Vector-Valued Modular Forms, SIGMA 15 (2019). · Zbl 1440.11060
[2]	[BK] J. Bruinier, M. Kuss, Eisenstein series attached to lattices and modular forms on orthogonal groups, Manuscripta Math. 106 (2001), 443-459. · Zbl 1002.11040
[3]	[BS] J. Bruinier, O. Stein, The Weil representation and Hecke operators for vector valued modular forms, 264 (2010), 249-270. · Zbl 1277.11034
[4]	[Br] J. Bruinier, On the converse theorem for Borcherds products, J. Algebra 397 (2014), 315-342. · Zbl 1296.11046
[5]	[McC] P. McCarthy, Introduction to Arithmetical Functions, Universitext, Springer-Verlag, (1986). · Zbl 0591.10003
[6]	[St] O. Stein, The Fourier expansion of Hecke operators for vactor-valued modular forms, Funct. Approx. Comment. Math. 52 (2015), 229-252. · Zbl 1398.11073