Успехи математических наук, 2024, том 79, выпуск 3(477), страница 194 DOI: https://doi.org/10.4213/rm10178 (Mi rm10178)

DOI: https://doi.org/10.4213/rm10178

Англоязычная версия:
Russian Mathematical Surveys, 2024, Volume 79, Issue 3, Pages 563
DOI: https://doi.org/10.4213/rm10178e

Реферативные базы данных:

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^1[x]1В русской версии статьи: 2-я строка снизу на с. 228. – Прим. ред. 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.

References
1.	Д. Р. Хис-Браун, “К теоремам Шевалле–Варнинга”, УМН, 66:2(398) (2011), 223–232          ; англ. пер.: D. R. Heath-Brown, “A note on the Chevalley–Warning theorems”, Russian Math. Surveys, 66:2 (2011), 427–435
2.	D. B. Leep, R. L. Petrik, “A correction and further improvements to the Chevalley–Warning theorems”, Finite Fields Appl., 96 (2024), 102427, 9 pp.

Цитирование в формате AMSBIB

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