Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2008; 45(6): 1635-1646

Printed November 1, 2008

Copyright © The Korean Mathematical Society.

Algebraic points on the projective line

Su-ion Ih

University of Colorado at Boulder

Abstract

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