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An Asymptotic Formula for a Sum of Products of Powers

Published online by Cambridge University Press:  20 November 2018

Ronald J. Evans
Ronald J. Evans*
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, California 920934
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Fix an integer r ≥ 2 and positive numbers b1, …, br. Write σ = b1+ …+br Let . In this note we evaluate the constant A (when it exists) for which

1

where the sum is over all vectors

2

We also obtain upper and lower bounds for the sum in (1).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 427 - 433
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Apostol, T. M., Introduction to analytic number theory, Springer-Verlag, N.Y., 1976.Google Scholar
2. Berndt, B. C., Problem 226, Canadian Math. Bull 19 (1976), 250-251.Google Scholar
3. Hewitt, E. and Stromberg, K., Real and abstract analysis, Springer-Verlag, N.Y., 1965.Google Scholar
4. Ireland, K. and Rosen, M., Elements of number theory, Bogden and Quigley, Tarrytown-on- Hudson, 1972.Google Scholar