Geodesic
The Circle Problem in an Arithmetic Progression
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 175-184

Voir la notice de l'article provenant de la source Cambridge University Press

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≤xn 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 
Smith, R.A. The Circle Problem in an Arithmetic Progression. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 175-184. doi: 10.4153/CMB-1968-019-2
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[1] 1. Estermann, T., An asymptotic formula in the theory of numbers, Proc. London Math. Soc. (2) 34 (1932) 280-292. Google Scholar

[2] 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] 3. Hooley, C., An asymptotic formula in the theory of numbers, Proc. London. Math. Soc. (3) 7 (1957) 396-413. Google Scholar

[4] 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] 5. Whittaker and Watson, Modern Analysis (4th edition, London, Cambridge, 1958). Google Scholar

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