Will a physicist prove the Riemann hypothesis?
نویسندگان
چکیده
منابع مشابه
Bernhard Riemann, a(rche)typical mathematical-physicist?
*Correspondence: Emilio Elizalde, Institut d’Estudis Espacials de Catalunya, Instituto de Ciencias del Espacio, CSIC, Campus UAB, Torre C5-Par-2a pl, 08193, Barcelona, Spain e-mail: [email protected] The work of Bernhard Riemann is discussed under the perspective of present day mathematics and physics, and with a prospective view toward the future, too. Against the (unfortunately rather wide...
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with s = 12 + it, and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching a proof, that in the range between 0 and T the function ξ(t) has about (T/2π) log(T/2π) − T/2π zeros. Riemann then continues “Man findet nun in der That etwa so viel reelle Wurzeln innerhalb dieser Grenzen, und es ist sehr wahrscheinlich, dass ...
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The Riemann zeta function ζ(s) is defined by ζ(s) = ∑∞ n=1 1 ns for R(s) > 1 and can be extended to a regular function on the whole complex plane deleting its unique pole at s = 1. The Riemann hypothesis is a conjecture made by Riemann in 1859 asserting that all non-trivial zeros for ζ(s) lie on the line R(s) = 12 , which is equivalent to the prime number theorem in the form of π(x)−Li(x) = O(x...
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ژورنال
عنوان ژورنال: Reports on Progress in Physics
سال: 2020
ISSN: 0034-4885,1361-6633
DOI: 10.1088/1361-6633/ab3de7