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Corrigendum and addendum

Published online by Cambridge University Press:  26 February 2010

H. Davenport  and
H. Halberstam
H. Davenport
Affiliation:
Trinity College, Cambridge and University of Nottingham.
H. Halberstam
Affiliation:
Trinity College, Cambridge and University of Nottingham.
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Extract

It has been pointed out to us by Professor L. Schoenfeld that there is a fallacy in the proof of Theorem 3 of our paper “The values of a trigonometrical polynomial at well spaced points” [ Mathematika, 13 (1966), 91–96]. The fallacy occurs in the appeal to Theorem 1 at the end of the proof. If this is to be made explicitly, we must not only put n = dn′ but also put q = dq′ but then the sum over m goes from 1 to q instead of from 1 to q′, and if one allows for this the final result becomes much weakened.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 229 - 232
Copyright
Copyright © University College London 1967

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References

page 229 note † For these facts, see for example Davenport, Multiplicative Number Theory (Markham, Chicago 1967), §5 and p. 148.Google Scholar

page 230 note † “The large sieve”, Mathematika, 14 (1967), 14–20, inequality (5).CrossRefGoogle Scholar

page 230 note ‡ See Ward, D. R., “Some series involving Euler's function”, London Math. Soc, 2 (1927), 210–214CrossRefGoogle Scholar, formula (2.2) with u = 1