Displaying similar documents to “On Sums of Squares and on Elliptic Curves over Function Fields”

Counting elliptic curves of bounded Faltings height

Ruthi Hortsch (2016)

Acta Arithmetica

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We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².

On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

Colloquium Mathematicae

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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...