Joshua Swidinsky

collaborators

3 papers

math.NT2024

Improved bounds for Serre's open image theorem

Imin Chen, Joshua Swidinsky

Let $E$ be an elliptic curve over the rationals which does not have complex multiplication. Serre showed that the adelic representation attached to $E / Q$ has open image, a…

math.NT2022

Sharper bounds for the error term in the Prime Number Theorem

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $ψ (x)$ to bounds of the same type on both $θ (x)$ and $π (x)$ .…

math.NT2022

Sharper bounds for the Chebyshev function $ψ (x)$

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We improve the unconditional explicit bounds for the error term in the prime counting function $ψ (x)$ . In particular, we prove that, for all $x > 2$ , we have \[ \left| ψ(x)-x \right|…

Improved bounds for Serre's open image theorem

Sharper bounds for the error term in the Prime Number Theorem

Sharper bounds for the Chebyshev function ψ(x)

Sharper bounds for the Chebyshev function $ψ (x)$