Tirukkannapuram Vijayaraghavan

Indian mathematician

Thirukannapuram Vijayaraghavan
Born	(1902-11-30)30 November 1902
Died	20 April 1955(1955-04-20) (aged 52)
Occupation	mathematician

Tirukkannapuram Vijayaraghavan (Tamil: திருக்கண்ணபுரம் விஜயராகவன்; 30 November 1902 – 20 April 1955) was an Indian mathematician from the Madras region. He worked with G. H. Hardy when he went to Oxford in mid-1920s on Pisot–Vijayaraghavan numbers. He was a fellow of Indian Academy of Sciences elected in the year 1934. His father was a pandit.

Vijayaraghavan was well versed in Sanskrit and Tamil. He was a close friend of André Weil. Weil hired him in 1930 despite his lack of diploma, and they served together in Aligarh Muslim University.^[1] While Weil was away in Europe, Ross Masood planned to replace Weil's professorship with Vijayaraghavan, but Vijayaraghavan quit in protest and moved to the University of Dhaka.^[2]

Vijayaraghavan proved a special case of Herschfeld's theorem on nested radicals:^[3] For $a_{n}>0$

{\sqrt {a_{1}+{\sqrt {a_{2}+{\sqrt {a_{3}+{\sqrt {a_{4}+\cdots }}}}}}}}

converges if and only if

{\overline {\lim }}(\log a_{n})/2^{n}<+\infty ,

where ${\overline {\lim }}$ denotes the limit superior.

References

^ Weil, André; Weil, André (1992). The apprenticeship of a mathematician. Basel Boston Berlin: Birkhäuser. ISBN 978-3-7643-2650-0.
^ M.S. Raghunathan, Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene.
^ Ramanujan, S. Collected Papers of Srinivasa Ramanujan (Ed. G. H. Hardy, P. V. S. Aiyar, and B. M. Wilson). Providence, RI: American Mathematical Society (2000), p. 348.