The Journal of the Indian Mathematical Society

S. Raghavan ¹

Affiliations
1 Tata Institute of Fundamental Research, Homi Bhabha Road,, Bombay 400005, IN

Abstract

Let T_n Denote the modular group of degree n, namely the group of 2n-rowed integral square matrices with n-rowed A, B, C, D satisfying the conditions AD' - BC' = E_n (the n-rowed identity matrix), AB' = BA' and CD'=DC', where, for any matrix P, its transpose is denoted by P'.

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S. Raghavan ¹, S. S. Rangachari ²

Affiliations
1 Tata Institute of Fundamental Research, Bombay 5 BR, IN
2 Centre of Advanced Study in Mathematics, University of Bombay, IN

Abstract

Let f(X, Y) = aX² + 2bXY + cY² be a positive definite binary quadratic form with rational integral coefficients a,b,c.

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S. Raghavan ¹

Affiliations
1 Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400005, IN

Abstract

Let r_m (t) denote the number of representations of a natural number t as a sum of m squares of integers. Then we have, for r_m (t) with m>4, the well-known asymptotic formula due to Hardy and Ramanujan [3].

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