English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $g>1$ be an integer and $f(X)\in{\mathbb Z}[X]$ a polynomial of positivedegree with no multiple roots, and put $u(n)=f(g^n)$. In this note, we studythe sequence of quadratic fields ${\mathbb Q}(\sqrt{u(n)}\,)$ as $n$ variesover the consecutive integers $M+1,\ldots,M+N$. Fields of this type includeShanks fields and their generalizations. Using the square sieve together withnew bounds on character sums, we improve an upper bound of Luca and Shparlinski(2009) on the number of $n \in \{M+1,\ldots,M+N\}$ with ${\mathbbQ}(\sqrt{u(n)}\,) = {\mathbb Q}(\sqrt{s}\,)$ for a given squarefree integer$s$.

On the number of distinct quadratic fields generated by the Shanks sequence