Geodesic
Reprint: On the number of integers which can be represented by a binary form (1938)
Documenta mathematica, Mahler Selecta (2019), pp. 475-481.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $F(x,y)$ be a binary form of degree $n\ge 3$ with integer coefficients and non-vanishing discriminant, and let $A(u)$ be the number of different positive integers $k\le u$, for which $|F(x,y)|=k$ has at least one solution in integers $x,y$. In this paper, using Mahler's $p$-adic generalisation of the Thue-Siegel theorem, Erdős and Mahler prove that
$\liminf_{u\to\infty} A(u)u^{-2/n}>0.$
\par Reprint of the authors' paper [J. Lond. Math. Soc. 13, 134--139 (1938; Zbl 0018.34401; JFM 64.0116.01)].
Classification : 11-03, 11E16, 11D85 
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     author = {Erd\H{o}s, P\'al and Mahler, Kurt},
     title = {Reprint: {On} the number of integers which can be represented by a binary form (1938)},
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     publisher = {mathdoc},
     volume = {Mahler Selecta},
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Erdős, Pál; Mahler, Kurt. Reprint: On the number of integers which can be represented by a binary form (1938). Documenta mathematica, Mahler Selecta (2019), pp. 475-481. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a26/