Marta Dujella

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math.NT2023

Uniform Bounds for the Number of Rational Points of Bounded Height on Certain Elliptic Curves

Marta Dujella

Let $E$ be an elliptic curve defined over a number field $k$ and $ℓ$ a prime integer. When $E$ has at least one $k$ -rational point of exact order $ℓ$ , we derive a uniform upp…

math.NT2023

Transcendence measure of $e^{1/ n}$

Marta Dujella, Anne-Maria Ernvall-Hytönen, Linda Frey +1

For a given transcendental number $ξ$ and for any polynomial $P (X) =: λ_{0} + \dots + λ_{k} X^{k} \in Z [X]$ , we know that $P (ξ) \neq = 0.$ Let $k \geq 1$ and $ω (k, H)$ be the infimum…

Uniform Bounds for the Number of Rational Points of Bounded Height on Certain Elliptic Curves

Transcendence measure of e1/n

Transcendence measure of $e^{1/ n}$