×

zbMATH — the first resource for mathematics

On Dirichlet characters of polynomials. (English) Zbl 1038.11052
The classical result, due to Pólya and Vinogradov, is that the estimates \[ \sum_{n=N+1}^{N+H}\chi(n)\ll q^{1/2}\log q \] holds for all nonprincipal Dirichlet characters \(\chi\) modulo \(q\). The main result of the note under review is to show that for certain primitive characters \(\chi\) modulo \(q\) and some special polynomials \(f(x)\) with integral coefficients an identity of the form \[ \left| \sum_{n=1}^{q}\chi\bigl(f(n)\bigr)\right| = q^{1/2} \] holds.

MSC:
11L10 Jacobsthal and Brewer sums; other complete character sums
11L40 Estimates on character sums
PDF BibTeX XML Cite
Full Text: DOI