On the number of divisors of a quaternary quadratic form (Q2810671)
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scientific article; zbMATH DE number 6589274
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of divisors of a quaternary quadratic form |
scientific article; zbMATH DE number 6589274 |
Statements
On the number of divisors of a quaternary quadratic form (English)
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3 June 2016
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quadratic form
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divisor function
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Hardy-Littlewood-Kloosterman method
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By improving a result of the second author [Acta Arith. 166, No. 2, 129--140 (2014; Zbl 1329.11105)] (who obtained the error term \(0(x^{7/2+\varepsilon})\)), the authors prove that NEWLINE\[NEWLINE\sum_{1\leq a,b,c,d\leq x}\tau(a^2+ b^2+ c^2+ d^2)= Ax^4\log x+ Bx^4+ O(x^3\log^7x),NEWLINE\]NEWLINE where \(\tau(n)\) denotes the divisor function, and \(A\), \(B\) are certain constants. The proof is based, among others on the Hardy-Littlewood-Kloosterman method.
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