Jaroslav Hanvcl

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20182026

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math.NT2026

Lower bounds for the Hausdorff dimension of expressible sets

Maiken Gravgaard, Simon Kristensen, Jaroslav Hančl

We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n = 1}^{\infty} \frac{1}{a _{n} b _{n}}$ , where $b_{n}$ satisfies som…

math.NT2024

On a Theorem of Legendre on Diophantine Approximation

Jaroslav Hančl, Tho Phuoc Nguyen

Legendre's theorem states that every irreducible fraction $\frac{p}{q}$ which satisfies the inequality $α - \frac{p}{q} < \frac{1}{2 q ^{2}}$ is convergent to $α$ . Later…

math.NT2018

Complementary Schur Asymptotics for Partitions

Jaroslav Hančl

We deduce from the strong form of the Hardy--Ramanujan asymptotics for the partition function $p (n)$ an asymptotics for $p_{- S} (n)$ , the number of partitions of $n$ that do not use…

math.NT2018

Metrical irrationality results related to values of the Riemann $ζ$ -function

Jaroslav Hančl, Simon Kristensen

We introduce a one-parameter family of series associated to the Riemann $ζ$ -function and prove that the values of the elements of this family at integers are linearly independent o…

Lower bounds for the Hausdorff dimension of expressible sets

On a Theorem of Legendre on Diophantine Approximation

Complementary Schur Asymptotics for Partitions

Metrical irrationality results related to values of the Riemann ζ-function

Metrical irrationality results related to values of the Riemann $ζ$ -function