ALGEBRAIC POINTS ON THE PROJECTIVE LINE

Title & Authors
ALGEBRAIC POINTS ON THE PROJECTIVE LINE
Ih, Su-Ion;

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 $\small{{\mathbb{P}}^1}$. 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 $\small{{\mathbb{P}}^1}$ according as the height bound goes to $\small{\infty}$.
Keywords
counting function;height;symmetric product;
Language
English
Cited by
1.
COUNTING MULTISECTIONS IN CONIC BUNDLES OVER A CURVE DEFINED OVER 𝔽q, International Journal of Number Theory, 2011, 07, 06, 1663
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