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On Absolute Lambert Sums

Published online by Cambridge University Press:  20 January 2009

Aurel Wintner
Aurel Wintner
Affiliation:
The Johns Hopkins University, Baltimore, Maryland, U.S.A.
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Let

be a series for which the Abelian generator,

converges whenever s > 0. Then the same is true of the Lambertian generator,

and vice versa.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , Issue 3 , December 1949 , pp. 128 - 132
Copyright
Copyright © Edinburgh Mathematical Society 1949

References

REFERENCES

[1]Hardy, G. H. and Littlewood, J. E., “On a Tauberian theorem for Lambert's series, and some fundamental theorems in the analytic theory of numbers,” Proc. London Math. Soc. (2), 19 (1921), 21–29.Google Scholar
[2]Whittaker, J. M., “The absolute summability of Fourier series,” Proc. Edinburgh Math. Soc. (2), 2 (1930–1931), 1–5.Google Scholar
[3]Wintner, A., “The sum formula of Euler-Maclaurin and the inversions of Fourier and Möbius,” American Journal of Mathematics, 69 (1947), 685–708.Google Scholar