Reassessing Riemann's Paper
On the Number of Primes Less Than a Given Magnitude
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Beschreibung
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.
Includes detailed explanation of the importance of Riemann’s zeta function Provides explicit calculations leading to the derivation of Riemann’s relation between prime numbers and zeros of Riemann’s function Emphasizes the importance of Riemann’s functional equation for mathematics and physics
Autor*in
Walter Dittrich
Themen in »Reassessing Riemann's Paper«
Riemann's Paper on Prime Numbers Zeta-function regularization Functional equation Fourier transform Riemann's function Mangoldt's formula Zeros of zeta function and critical strip History of prime number theory