Lectures on a Method in the Theory of Exponential Sums
by M. Jutila
Publisher: Tata Institute of Fundamental Research 1987
Number of pages: 134
It was my first object to present a selfcontained introduction to summation and transformation formulae for exponential sums involving either the divisor function d(n) or the Fourier coefficients of a cusp form; these two cases are in fact closely analogous. Secondly, I wished to show how these formulae can be applied to the estimation of the exponential sums in question.
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by W W L Chen - Macquarie University
These notes were used by the author at Imperial College, University of London. The contents: arithmetic functions, elementary prime number theory, Dirichlet series, primes in arithmetic progressions, prime number theorem, Riemann zeta function.
by J.I. Igusa - Tata Institute of Fundamental Research
One of the principal objectives of modern number theory must be to develop the theory of forms of degree more than two,to the same satisfactory level in which the theory of quadratic forms is found today as the work of eminent mathematicians.
by Henri Cohen - arXiv.org
Contents: Functional Equations; Elliptic Functions; Modular Forms and Functions; Hecke Operators: Ramanujan's discoveries; Euler Products, Functional Equations; Modular Forms on Subgroups of Gamma; More General Modular Forms; Some Pari/GP Commands.
by R. D. Carmichael - John Wiley & Sons
The author's purpose has been to supply the reader with a convenient introduction to Diophantine Analysis. No attempt has been made to include all special results, but a large number of them are to be found both in the text and in the exercises.