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On the Riemann Zeta‐Function
Author(s) -
Littlewood J. E.
Publication year - 1926
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s2-24.1.175
Subject(s) - riemann zeta function , citation , riemann hypothesis , function (biology) , mathematics , computer science , calculus (dental) , combinatorics , library science , pure mathematics , medicine , dentistry , evolutionary biology , biology
As we've seen in a previous homework, the attempt to compute finite sums by inverting the difference operator inevitably led Jacob Bernoulli to consider the Taylor series of a curious function: z e z − 1 = k≥0 B k z k k! , whose coefficients B k are now called the Bernoulli numbers. He used this technology to compute finite sums like 1 p + · · · + n p. However, he was stumped by infinite sums like 1 −2 + 2 −2 + 3 −2 + · · · and this led him to pose the famous Basel problem: namely, to compute this sum! In 1735, a young fellow named Euler stunned the mathematical world by cracking the Basel problem and showing