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The Circle Problem in an Arithmetic Progression

Published online by Cambridge University Press:  20 November 2018

R.A. Smith
R.A. Smith*
Affiliation:
University of Toronto
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In following a suggestion of S. Chowla to apply a method of C. Hooley [3] to obtain an asymptotic formula for the sum ∑ r(n)r(n+a), where r(n) denotes the number of representations of n≤x

n as the sum of two squares and is positive integer, we have had to obtain non-trivial estimates for the error term in the asymptotic expansion of

1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 175 - 184
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Estermann, T., An asymptotic formula in the theory of numbers, Proc. London Math. Soc. (2) 34 (1932) 280-292.Google Scholar
2. Estermann, T., On the representations of a number as the sura of two products, Proc. London Math. Soc. (2) 31 (1930) 123-133.Google Scholar
3. Hooley, C., An asymptotic formula in the theory of numbers, Proc. London. Math. Soc. (3) 7 (1957) 396-413.Google Scholar
4. Mordell, L. J., On the number of solutions in incomplete residue sets of quadratic congruences, Arch, der Math. 8(1957) 153-157.Google Scholar
5. Whittaker and Watson, Modern Analysis (4th edition, London, Cambridge, 1958).Google Scholar