The Journal of the Indian Mathematical Society

K. Ananda Rao ¹

Affiliations
1 29, Boag Koad, Madras 17, IN

Abstract

The quadratic forms which are mainly dealt with in this paper are

a(x²+y²)+C(z² + t²), (1)

a(x² + y²)+2c(z² + t²), (2)

where x, y, z, t are integer variables and the constant coefficients a, c are unequal odd positive primes.

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K. Ananda Rao ¹

Affiliations
1 29, Boag Road, Thyagarayanagar, Madras, IN

Abstract

In a paper published recently in this Journal [1] I gave a theorem on the construction of quasi-elliptic functions, that is, functions f(u) of a complex variable u which are meromorphic and satisfy the functional relations f(u + 2ω) = Kf(u), f(u + 2ω') = K'f(u), where K, K', ω, ω' are constants, the ratio of ω' to ω not being real.

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K. Ananda Rao ¹

Affiliations
1 Thyagarayanagar, Madras 17, IN

Abstract

Hermite, in the course of his investigations in the theory of elliptic functions, was led to introduce certain related functions which he called doubly periodic functions of the second kind.

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K. Ananda Rao

Abstract

In the first of a series of important papers communicated to the London Mathematical Society, Hardy proved the following:

THEOREM: If Σa_n is summable (C1) to sum s, and if

a_n = O(1/n),

then Σa_n converges to sum s.

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