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 K. Chandrasekharan - Tata Institute of Fundamental Research
These notes provide an intorduction to the theory of the Riemann Zeta-function for students who might later want to do research on the subject. The Prime Number Theorem, Hardy's theorem, and Hamburger's theorem are the principal results proved here.
by William Duke, Yuri Tschinkel - American Mathematical Society
The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.
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.