The Journal of the Indian Mathematical Society

M. Bhaskaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

The summation of singular series associated with a quadratic form is closely connected with the problem of finding the number of representations of a given positive number in that form.

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M. Bhaskaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras-5, IN

Abstract

In the preceding paper [3], I have summed up the singular series associated with the representation of a given integer n in the quadratic form.

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M. Bhaskaran ¹

Affiliations
1 Ramanujan Institute, Madras 5, IN

Abstract

In this paper, I give two applications of the following result of Chowla [2]:

Let {m, n} denote the number of different pairs of numbers x, y such that (x, y) = 1, 1 ≤ x ≤ m, 1 ≤ y ≤ n.

Then

{m, n} = 6mn/π² + O(m log n) if m ≥ n.

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