Geodesic
Pair Correlation of Squares in $p$ -Adic Fields
Canadian journal of mathematics, Tome 55 (2003) no. 2, pp. 432-448

Voir la notice de l'article provenant de la source Cambridge University Press

Let $p$ be an odd prime number, $K$ a $p$ -adic field of degree $r$ over ${{\mathbf{Q}}_{p}}$ , $O$ the ring of integers in $K,\,B\,=\,\{{{\beta }_{1}},\ldots .{{\beta }_{r}}\}$ an integral basis of $K$ over ${{\mathbf{Q}}_{p}}$ , $u$ a unit in $O$ and consider sets of the form $N\,=\,\{{{n}_{1}}{{\beta }_{1}}\,+\ldots +\,{{n}_{r}}{{\beta }_{r}}\,:\,1\,\le \,{{n}_{j}}\,\le \,{{N}_{j}},\,1\,\le \,j\,\le \,r\}$ . We show under certain growth conditions that the pair correlation of $\{u{{z}^{2}}\,:\,z\,\in N\}$ becomes Poissonian.
DOI : 10.4153/CJM-2003-019-6
Mots-clés : 11S99, 11K06 
Zaharescu, Alexandru. Pair Correlation of Squares in $p$ -Adic Fields. Canadian journal of mathematics, Tome 55 (2003) no. 2, pp. 432-448. doi: 10.4153/CJM-2003-019-6
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