arXiv subjects

Simon L Rydin Myerson

Publications and source records attributed to Simon L Rydin Myerson.

2 recordsLinked to original sources

arXiv2025

Expander estimates for cubes

If $\mathscr A$ is a set of natural numbers of exponential density $δ$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 δ)$. This is a considerable improvement on the previous best lower bounds for this problem, obtained by Davenport more than 80 years ago. The result is the best possible for $δ\ge \frac 45$.

math.NT↗

arXiv2023

A question about points on an elliptic curve with prime denominator

Let E be an elliptic curve defined by a Weierstrass equation with integer coefficients. Any rational point on E other than the identity is of the form $ ( x(P) / z(P)^2 , y(P) / z(P)^3 ) $ where $ x(P), y(P) \in \mathbb Z $ and $ z(P) \in \mathbb N $ and in addition both $ \gcd( x(P) , z(P) ) = 1 $ and $ \gcd( y(P) , z(P) ) = 1 $ hold. The question is: how often is $ z(P) $ a prime number?

math.NT↗