André Weil: His Book on Number Theory and Indian References

B. S. Yadav ()

A chapter in Ancient Indian Leaps into Mathematics, 2009, pp 55-61 from Springer

Abstract: Summary After giving a brief description of André Weil as a man and mathematician, the article concentrates on his book Number Theory: An Approach Through History, and particularly on Chap.IX, in which he discusses the history and the solution of Pell’s equation. It is shown that it was the Indian mathematician Brahmagupta who first attempted to solve the equation, in the seventh century c.e. He defined a binary composition on the set of all solutions of the equation, a work of genuine ingenuity, leading to the result that if the equation has a nontrivial solution, then it has infinitely many such solutions. Lagrange showed that the equation does indeed have a nontrivial solution, and Dirichlet later solved the equation completely.

Keywords: Nontrivial Solution; Riemann Hypothesis; Binary Composition; Transcendental Number; General Riemann Hypothesis (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4695-0_4

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DOI: 10.1007/978-0-8176-4695-0_4

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