Abstract
We describe an algorithm for computing the inner product between a holomorphic modular form and a unary theta function, in order to determine whether the form is orthogonal to unary theta functions without needing a basis of the entire space of modular forms and without needing to use linear algebra to decompose this space completely.
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Acknowledgements
The research of the first author was supported by grant project numbers 27300314, 17302515, and 17316416 of the Research Grants Council.
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Kane, B., Man, S.H. (2017). The Bruinier–Funke Pairing and the Orthogonal Complement of Unary Theta Functions. In: Bruinier, J., Kohnen, W. (eds) L-Functions and Automorphic Forms. Contributions in Mathematical and Computational Sciences, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-69712-3_8
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DOI: https://doi.org/10.1007/978-3-319-69712-3_8
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