Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-18T07:34:14.831Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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