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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Reassessing Riemann's Paper/ by Walter Dittrich.
其他題名:	On the Number of Primes Less Than a Given Magnitude /
作者:	Dittrich, Walter.
面頁冊數:	XIX, 65 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-319-91482-4
ISBN:	9783319914824

Reassessing Riemann's Paper = On the Number of Primes Less Than a Given Magnitude /
Dittrich, Walter.

Reassessing Riemann's PaperOn the Number of Primes Less Than a Given Magnitude /[electronic resource] :by Walter Dittrich. - 1st ed. 2018. - XIX, 65 p. 4 illus.online resource. - SpringerBriefs in History of Science and Technology,2211-4564. - SpringerBriefs in History of Science and Technology,.

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 -- Supplements -- Appendix.

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.

ISBN: 9783319914824

Standard No.: 10.1007/978-3-319-91482-4doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA21-27

Dewey Class. No.: 510.9

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