Pillars of Transcendental Number Theory (PDF)

Saradha Natarajan is an INSA Senior Scientist at the DAE Center for Excellence in Basic Sciences (CEBS) at the University of Mumbai. Earlier, she was a Professor of Mathematics at the Tata Institute of Fundamental Research, Mumbai, until 2016. She was a postdoctoral fellow at Concordia University, Canada; Macquarie University, Australia; National Board of Higher Mathematics (NBHM), India. She is an elected fellow of the Indian National Science Academy (INSA). She obtained her Ph.D. in 1983 under the guidance of Professor T. S. Bhanumurthy from Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai.

>1) successive terms from arithmetic progression with common difference d is cube or higher power only for d large. She has also made significant contributions to Thue equations and Diophantine approximations, especially towards conjectures of Bombieri, Mueller and Schmidt on number of solutions of Thue inequalities for forms in terms of number of non-zero coefficients of the form. Using new induction technique, an old result of Siegel on the number of primitive solutions of Thue inequalities was improved significantly. In the area of transcendence, she has obtained best possible simultaneous approximation measures for values of exponential function and Weierstarss elliptic function. Further, significant lower bounds were shown for the Ramanujan tau-function for almost all primes p. Some problems in elementary number theory have also attracted her attention, for example on a conjecture of Pomerance on residue systems and its generalizations. It is shown that 2, 3, 7 are the only primes p for which there exist p consecutive primes forming complete residue system mod p. She has collaborated with many mathematicians both in India and abroad and guided students for Ph.D. and graduation. She has travelled widely and given invited talks and lectures at seminars and conferences.

Ravindranathan Thangadurai is Professor at