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Dirichlet Series

المؤلف:  Bohr, H.

المصدر:  "Zur Theorie der allgemeinen Dirichletschen Reihen." Math. Ann. 79

الجزء والصفحة:  ...

23-8-2020

1375

Dirichlet Series

A series

where  and  are complex and {lambda(n)}" src="https://mathworld.wolfram.com/images/equations/DirichletSeries/Inline3.gif" style="height:15px; width:35px" /> is a monotonic increasing sequence of real numbers. The numbers  are called the exponents, and  are called the coefficients. When , then , the series is a normal Dirichlet L-series. The Dirichlet series is a special case of the Laplace-Stieltjes transform.

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REFERENCES:

Apostol, T. M. "General Dirichlet Series and Bohr's Equivalence Theorem." Ch. 8 in Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 161-189, 1997.

Bohr, H. "Zur Theorie der allgemeinen Dirichletschen Reihen." Math. Ann. 79, 136-156, 1919.