Cooper and Lam's conjecture for generalized Bell ternary quadratic forms (Q495269)
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scientific article; zbMATH DE number 6479837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cooper and Lam's conjecture for generalized Bell ternary quadratic forms |
scientific article; zbMATH DE number 6479837 |
Statements
Cooper and Lam's conjecture for generalized Bell ternary quadratic forms (English)
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9 September 2015
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Bell's theorem determines the counting function of the ternary quadratic forms \(x^2 +by^2 +cz^2\), with \(b, c \in \{1, 2, 4, 8\}, \) in terms of the number \(r_3(n) \) of representations of \(n\) as a sum of three squares. The author verifies the conjecture of \textit{S. Cooper} and \textit{H. Y. Lam} [J. Number Theory 133, No. 2, 719--737 (2013; Zbl 1309.11022)]. This result includes two new cases so far left open.
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sum of squares
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ternary quadratic form
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theta function
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Hurwitz three-squares formula
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Cooper and Lam's conjecture
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