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**public sources and our publisher partners.**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.

We study the computational complexity of emptiness problems for circuits over sets of natural numbers with the operations union, intersection, complement, addition, and multiplication. For most… Expand

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

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

Abstract We study the computational complexity of emptiness problems for circuits over sets of natural numbers with the operations union, intersection, complement, addition, and multiplication. For… Expand

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

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

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

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