In the second half of 2015, the American Math Society will publish a five volume (total about 3000 pages) set of books that is a graduate analysis text with lots of additional bonus material. Included are hundreds of problems and copious notes which extend the text and provide historical background. Efforts have been made to find simple and elegant proofs and to keeping the writing style clear.
Conformal metric methods, topics in analytic number theory, Fuchsian ODEs and associated special functions, asymptotic methods, univalent functions, Nevanlinna theory.
Selected topics include Poincaré metric, Ahlfors-Robinson proof of Picard’s theorem, Bergmann kernel, Painlevé’s conformal mapping theorem, Jacobi 2- and 4-squares theorems, Dirichlet series, Dirichlet’s prime progression theorem, zeta function, prime number theorem, hypergeometric, Bessel and Airy functions, Hankel and Sommerfeld contours, Laplace’s method, stationary phase, steepest descent, WKB, Koebe function, Loewner evolution and introduction to SLE, Nevanlinna’s First and Second Main theorems.