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The least prime number in a Beatty sequence

- J. Steuding, Marc Technau
- Mathematics
- 28 December 2015

Abstract We prove an upper bound for the least prime in an irrational Beatty sequence. This result may be compared with Linnik's theorem on the least prime in an arithmetic progression.

Emptiness Problems for Integer Circuits

- D. Barth, Moritz Beck, Titus Dose, Christian Glaßer, Larissa Michler, Marc Technau
- Mathematics, Computer Science
- MFCS
- 2017

TLDR

Metric results on summatory arithmetic functions on Beatty sets

- Marc Technau, Agamemnon Zafeiropoulos
- Mathematics
- 13 July 2019

Let $f\colon\mathbb{N}\rightarrow\mathbb{C}$ be an arithmetic function and consider the Beatty set $\mathcal{B}(\alpha) = \lbrace\, \lfloor n\alpha \rfloor : n\in\mathbb{N} \,\rbrace$ associated to a… Expand

Modular hyperbolas and Beatty sequences

- Marc Technau
- Mathematics
- 1 August 2018

Bounds for $\max\{m,\tilde{m}\}$ subject to $m,\tilde{m} \in \mathbb{Z}\cap[1,p)$, $p$ prime, $z$ indivisible by $p$, $m\tilde{m}\equiv z\bmod p$ and $m$ belonging to some fixed Beatty sequence $\{… Expand

Emptiness problems for integer circuits

- D. Barth, Moritz Beck, Titus Dose, Christian Glaßer, Larissa Michler, Marc Technau
- Mathematics, Computer Science
- Theor. Comput. Sci.
- 6 July 2020

TLDR

A Loewner Equation for Infinitely Many Slits

- Marc Technau, Niclas Technau
- Mathematics
- 1 June 2017

It is well-known that the growth of a slit in the upper half-plane can be encoded via the chordal Loewner equation, which is a differential equation for schlicht functions with a certain… Expand

Kloosterman sums with twice-differentiable functions.

- I. Shparlinski, Marc Technau
- Mathematics
- 15 February 2019

We bound Kloosterman-like sums of the shape \[ \sum_{n=1}^N \exp(2\pi i (x \lfloor f(n)\rfloor+ y \lfloor f(n)\rfloor^{-1})/p), \] with integers parts of a real-valued, twice-differentiable function… Expand

The maximal order of iterated multiplicative functions

- C. Elsholtz, Marc Technau, Niclas Technau
- Mathematics
- 14 September 2017

Following Wigert, various authors, including Ramanujan, Gronwall, Erdős, Ivic, Schwarz, Wirsing, and Shiu, determined the maximal order of several multiplicative functions, generalizing Wigert's… Expand

On the distribution of $\alpha p$ modulo one in imaginary quadratic number fields with class number one.

- S. Baier, Marc Technau
- Mathematics
- 18 May 2019

We investigate the distribution of $\alpha p$ modulo one in imaginary quadratic number fields $\mathbb{K}\subset\mathbb{C}$ with class number one, where $p$ is restricted to prime elements in the… Expand

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