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Note on the region of overconvergence of Dirichlet series with Ostrowski gaps

Published online by Cambridge University Press:  18 May 2009

J. P. Earl  and
J. R. Shackell
J. P. Earl
Affiliation:
University of Kentat Canterbury
J. R. Shackell
Affiliation:
University of Kentat Canterbury
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The main object of this note is to show that a proof given by A. J. Macintyre [2] of a result on the overconvergence of partial sums of power series works more easily in the context of Dirichlet series. Applying this observation to the particular Dirichlet series Σane−ns, we can remove certain restrictions which Macintyre finds necessary in the direct treatment of power series.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 169 - 173
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

1.Bourion, G., L'ultraconvergence dans les séries de Taylor, Actualités Scientifiques et Industrielles no. 472 (Paris 1937).Google Scholar
2.Macintyre, A. J., An overconvergence theorem of G. Bourion and its application to coefficients of certain power series, Ann. Acad. Sci. Fenn. Ser. A.I. 250/23 (1958).Google Scholar