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Note on the Hardy-Landau Summation Formula

Published online by Cambridge University Press:  20 November 2018

T. L. Pearson
T. L. Pearson*
Affiliation:
University of Saskatchewan
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Broadly speaking, the Hardy-Landau summation formula * is given by

where r(n) is the number of integer solutions of the Diophantine equation x2 + y2 = n, and f(x) and g(x) are transforms with respect to the Watson kernel that is:

and

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 717 - 720
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Fox, C., Chain transforms, Proc. Am. Math. Soc.,5 (1954), 677-688.Google Scholar
2. Guinand, A. P., Summation formulae and self-reciprocal functions, Quart. J. Math.,9 (1938), 53-67.Google Scholar
3. Landau, E., Vorlesungen űber Zahlentheorie, Band 2, Leipzig, 1927.Google Scholar
4. Miller, J. B., A symmetrical convergence theory for general transforms, Proc. London Math. Soc., (3),8 (1958), 224-241.Google Scholar