Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56 (Q6107497)
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scientific article; zbMATH DE number 7706228
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56 |
scientific article; zbMATH DE number 7706228 |
Statements
Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56 (English)
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3 July 2023
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In the paper under review, mainly the theta functions of nineteen positive-definite integral non-diagonal quaternary quadratic forms of discriminant 784 with levels 28 or 56 are investigated. These theta functions are expressed in terms of Eisenstein series and cusp forms. Using these functions, explicit formulas for the representation number of a positive integer n by their corresponding non-diagonal quaternary quadratic forms are obtained. Theta functions of the genera to which those non-diagonal quaternary quadratic forms belong are found. The theta function of each non-diagonal quadratic form in terms of the theta functions of certain diagonal quaternary quadratic forms and a cusp form is determined.
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theta function
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modular form
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genus of a quaternary quadratic form
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class of a quaternary quadratic form
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representation number
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Dedekind eta function
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eta quotient
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