J. Korean Math. Soc. 2008; 45(6): 1635-1646
Printed November 1, 2008
Copyright © The Korean Mathematical Society.
Su-ion Ih
University of Colorado at Boulder
Schanuel's formula describes the distribution of $rational$ points on projective space. In this paper we will extend it to $algebraic$ points of bounded degree in the case of ${\mathbb{P}}^{1}$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a $quasi$-$asymptotic$ formula for the number of points of bounded degree on ${\mathbb{P}}^{1}$ according as the height bound goes to $\infty$.
Keywords: counting function, height, symmetric product
MSC numbers: 11G35, 11G50, 14G05
2011; 48(6): 1171-1187
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