Lectures on Mathematics and Physics. Mathematics. Tata Institute of Fundamental Research. 85. Berlin: Springer-Verlag. Bombay: Tata Institute of Fundamental Research, xiii, 169 p. DM 44.00; öS 321.20; sFr 44.00 (1995).
This book presents a connected account of the author’s many works on upper and lower bounds for
and related integrals. Although most of these results have therefore appeared before, it is convenient to have them collected together, with the proofs based on common principles, which are established here in the first two chapters.
The statements of many of the theorems are long and involved. As two pithy examples we mention: (1) Let be a complex number of modulus 1, and let with a sufficiently large constant . Then
(2) If with constant, then
for any positive integer .