03207oam 2200457 450 99646640910331620210610141702.03-030-61049-710.1007/978-3-030-61049-4(CKB)5460000000008706(DE-He213)978-3-030-61049-4(MiAaPQ)EBC6450961(PPN)253254574(EXLCZ)99546000000000870620210610d2018 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierReassessing Riemann's paper on the number of primes less than a given magnitude /Walter DittrichSecond edition.Cham, Switzerland :Springer,[2018]©20181 online resource (XI, 107 p. 18 illus., 10 illus. in color.) SpringerBriefs in History of Science and Technology3-030-61048-9 Preface -- Introduction -- Short Biography of Bernhard Riemann (1826 – 1866) -- Towards Euler's Product Formula and Riemann’s Extension of the Zeta Function -- Prime Power Number Counting Function -- Riemann as an Expert in Fourier Transforms -- On the Way to Riemann’s Entire Function ζ(s) -- The Product Representation of ξ(s) and ζ(s) by Riemann (1859) -- Derivation of Von Mangoldt’s Formula for ψ(x) -- The Number of Roots in the Critical Strip -- Riemann’s Zeta Function Regularization -- ζ-Function Regularization of the Partition Function of the Harmonic Oscillator -- ζ-Function Regularization of the Partition Function of the Fermi Oscillator -- The Zeta-Function in Quantum Electrodynamics (QED) -- Summary of Euler-Riemann Formulae -- Appendix.In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann’s only work on prime numbers, including ideas – new at the time – such as analytical continuation into 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. This revised and enhanced new edition contains three new chapters, two on the application of Riemann’s zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.SpringerBriefs in history of science and technology.Number theoryNumber theory.512.7Dittrich Walter46017MiAaPQMiAaPQUtOrBLWBOOK996466409103316Reassessing Riemann's Paper1563734UNISA01580nam0-2200445 --450 991032695610332120251121125308.0978-88-917-8128-420190705d2019----kmuy0itay5050 baitafreITa a 001yyDisegnare un mondo miglioreil campus universitario di Oscar Niemeyer a Constantine= Dessiner un monde meilleurle campus universitaire d'Oscar Niemeyer à ConstantineFrancesco Felice Buonfantino, Alessandra PaglianoMilanoFrancoAngeli2019170 p.ill.23 cmSerie di architettura e design111Contiene testi in italiano o franceseBibliografia: p. 165-166Dessiner un monde meilleurle campus universitaire d'Oscar Niemeyer à ConstantineNiemeyer, OscarCampusConstantine (Algeria)727.309223Buonfantino,Francesco Felice765321Pagliano,Alessandra289597ITUNINAREICATUNIMARCBK9910326956103321B 1664 CAN045/2019DARPUB 1665 CAN046/2019DARPU12.1507303/19DARST12.1513313/19DARSTARCH B 3245702/2019FARBCARCH B 3346171/2020FARBCXXXI VARIE 619244/2020FSPBCFSPBCFARBCDARSTDARPUDisegnare un mondo migliore1555414UNINA