Andreas J. Weingartner

activity

20082023

most citedZeros of Dirichlet series with periodic coefficients

29 citations · 32 across the 8 of their papers we have counts for

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Showing 2015Show all

3 papers · 1 filter

math.NT2015

On integers $n$ for which $X^{n} - 1$ has a divisor of every degree

Carl Pomerance, Lola Thompson, Andreas Weingartner

A positive integer $n$ is called $φ$ -practical if the polynomial $X^{n} - 1$ has a divisor in $Z [X]$ of every degree up to $n$ . In this paper, we show that the count of $φ$ -pr…

math.NT2015

An explicit polynomial analogue of Romanoff's theorem

Igor E. Shparlinski, Andreas J. Weingartner

Given a polynomial $g$ of positive degree over a finite field, we show that the proportion of polynomials of degree $n$ , which can be written as $h + g^{k}$ , where $h$ is an irreducibl…

math.NT2015★ 2 cited

On the degrees of polynomial divisors over finite fields

Andreas Weingartner

We show that the proportion of polynomials of degree $n$ over the finite field with $q$ elements, which have a divisor of every degree below $n$ , is given by $c_q n^{-1} + O(n^{-2}…

On integers n for which Xn−1 has a divisor of every degree

An explicit polynomial analogue of Romanoff's theorem

On the degrees of polynomial divisors over finite fields

On integers $n$ for which $X^{n} - 1$ has a divisor of every degree