Topics in Complex Analysis
À propos de cet ebook
Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 — a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022.
The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
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Quelques mots sur l'auteur
Dan Romik is a professor of mathematics at the University of California, Davis. His research interests include combinatorics, number theory, probability theory, asymptotic analysis, and more. His 2016 paper on the moving sofa problem, an unsolved problem in geometry asking what is the largest piece of two-dimensional furniture that can be moved around a corner in an L-shaped hallway, was featured in news articles from media outlets in the UK, US, South Korea, and the Netherlands, and was a subject of a video on the popular online video channel Numberphile. His previous book, The Surprising Mathematics of Longest Increasing Subsequences, was published in 2015.
