Russian Mathematical Surveys, 2024, Volume 79, Issue 3, Pages 563 DOI: https://doi.org/10.4213/rm10178e (Mi rm10178)

DOI: https://doi.org/10.4213/rm10178e

Russian version:
Uspekhi Matematicheskikh Nauk, 2024, Volume 79, Issue 3(477), Page 194
DOI: https://doi.org/10.4213/rm10178

Bibliographic databases:

I have learned of an error in my paper [1], namely in the proof of part (iii) of Theorem 2. On line 10 of page 432 it is claimed that $\mathscr{N}(L')=1+(q-1)\mathscr{N}(L)$, but this is not necessarily true.

An explanation of the error, and a proof of a slightly stronger version of Theorem 2 (iii), is given by Leep and Petrik [2]. The author is grateful to Pete Clark for pointing out this error, and to David Leep and Rachel Petrik for informing me of their alternative treatment.

Bibliography
1.	D. R. Heath-Brown, “A note on the Chevalley–Warning theorems”, Russian Math. Surveys, 66:2 (2011), 427–435
2.	D. B. Leep and R. L. Petrik, “A correction and further improvements to the Chevalley–Warning theorems”, Finite Fields Appl., 96 (2024), 102427, 9 pp.

Citation in format AMSBIB

\Bibitem{Hea24}
\by D.~R.~Heath-Brown
\paper Letter to the editors
\jour Russian Math. Surveys
\yr 2024
\vol 79
\issue 3
\pages 563
\mathnet{http://mi.mathnet.ru//eng/rm10178}
\crossref{https://doi.org/10.4213/rm10178e}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4801221}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024RuMaS..79..563H}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001347820700002}