Contributions to algebraic number theory from India: From independence to late 90’s

Dipendra Prasad ()
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Dipendra Prasad: Tata Institute of Fundamental Research

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 3, 779-793

Abstract: Abstract There was a conference organised at the Institite of Mathematical Sciences, Chennai in 1997 on the occasion of the 50th anniversary of India’s Independence to review contributions by Indians to various branches of mathematics since Independence. This is a written account of the lecture I gave then on some of the contributions by Indian mathematicians to Algebraic number theory from India’s independence to late 90’s. There has been a lot of work done in India during these years, and it will be impossible to report on all of it in limited space. We have therefore chosen some of the representative works from the vast literature reflecting to some extent the author’s taste. Since this was a report about work done in the country, works of several very prominent mathematicians from India during this period who worked for most of their scientific career outside India has been omitted. In particular, we do not speak about the work of S. Chowla who has contributed so much to so many areas of Algebraic number theory. We have also restricted ourselves to areas very closely related to Algebraic number theory, and have therefore omitted topics in transcendental and analytic number theory which was reported by others in the conference. We have also omitted from our consideration the arithmetic theory of algebraic groups. In particular, we do not speak on the work of K.G. Ramanathan who initiated the study of arithmetic groups in the country which has flourished into a very strong area of research at the Tata Institute of Fundamental Research, Mumbai. We begin the report by listing the two major schools in the country where algebraic number theory has been pursued, and in each case list some of the mathematicians from these schools. Limitation of knowledge on the part of the author has prevented him from a more complete list. In the list below, non-Indian mathematicians have been put in a bracket, and Y is on the immediate right of X, if Y is a student of X.

Keywords: Warings problem; geometry of numbers; quadratic forms; Oppenheim conjecture; modular forms; Siegel modular forms; half integral weight forms; Siegel Ramachandra units (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0354-3

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