Reassessing Riemann's Paper On the Number of Primes Less Than a Given Magnitude /

• Κύριος συγγραφέας: Dittrich, Walter (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: SpringerBriefs in History of Science and Technology,
• Θέματα: Mathematics.; History.; Number theory.; Quantum field theory.; String theory.; History of Mathematical Sciences.; Number Theory.; Quantum Field Theories, String Theory.
• Φυσική περιγραφή: XIX, 65 p. 4 illus. online resource.
• ISBN: 9783319914824
• ISSN: 2211-4564
• DOI: 10.1007/978-3-319-91482-4

In this book, the author pays tribute to Bernhard Riemann (1826-1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann's only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann's ideas on regularizing infinite values in field theory is also emphasized.