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Dirichlet series with independent and identically distributed coefficients

Published online by Cambridge University Press:  24 October 2008

L. E. Clarke
L. E. Clarke
Affiliation:
School of Mathematics and Physics, University of East Anglia
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Extract

Let be a Dirichlet series. Then it is known that if is divergent, the abscissa of convergence σ1 is given by

and that if is divergent, the abscissa of absolute convergence σ2 is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 393 - 397
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

1Loève, M.Probability theory (3rd edition; Van Nostrand, 1963).Google Scholar
2Titchmarsh, E. C.The theory of functions (2nd edition; Oxford University Press, 1939).Google Scholar