A survey of investigations of the discrete ergodic method in number theory (Q2857773)
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scientific article; zbMATH DE number 6228983
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A survey of investigations of the discrete ergodic method in number theory |
scientific article; zbMATH DE number 6228983 |
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19 November 2013
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ternary quadratic forms
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discrete ergodic method
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asymptotic formulae for the number of representations of an integer by quadratic forms
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A survey of investigations of the discrete ergodic method in number theory (English)
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The author describes some applications of the discrete ergodic method (DEM) to find asymptotic formulae for the number of representations of an integer by ternary (or \(n-\)ary with \(n \geq 3\)) quadratic forms. DEM is explained at the example of the form \(x_1^2+x_2^2+x_3^2\) along the lines of \textit{Yu. V. Linnik}'s 1940 paper [Bull. Acad. Sci. URSS, Ser. Math. (Izv. Akad. Nauk SSSR) 4, No. 4-5, 363--402 (1940; Zbl 0024.25001)]. Then several results obtained by using a variant of the method are presented. All these results were published before 1991 with the exception of three author's papers published later. The paper ends with a list of six open problems on ternary quadratic forms, where DEM should be applicable.
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