An Introduction to Modular Forms
by Henri Cohen
Publisher: arXiv.org 2018
Number of pages: 58
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.
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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.
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In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. Contents: Formal Power Series; Analysis; Analytic theory of partitions; Representation by squares.
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The aim of these lectures is to introduce the readers to the most fascinating aspects of the fruitful unifications of sieve methods and analytical means which made possible such deep developments in prime number theory ...
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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.