A remark on the behavior of theta series of degree \(n\) under modular transformations (Q2734542)
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scientific article; zbMATH DE number 1634470
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on the behavior of theta series of degree \(n\) under modular transformations |
scientific article; zbMATH DE number 1634470 |
Statements
16 August 2001
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theta series
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Siegel modular forms
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Jacobi-like forms
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A remark on the behavior of theta series of degree \(n\) under modular transformations (English)
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Generalizing earlier works of \textit{A. N. Adrianov} and \textit{G. M. Maloletkin} [Proc. Steklov Inst. Math. 148, 1--12 (1980; Zbl 0443.10023)] the author investigates the behavior of a general type of theta series with respect to indefinite quadratic forms under modular substitutions. These theta series can be used to construct a generalization of Jacobi-like forms in the sense of \textit{D. Zagier} [Proc. Indian Acad. Sci., Math. Sci. 104, 57--75 (1994; Zbl 0806.11022)]. Moreover a method of constructing Siegel modular forms from these theta series is provided.
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