Lyndon words, polylogarithms and the Riemann ζ function
نویسندگان
چکیده
منابع مشابه
Riemann ’ s ζ - Function
We provide an overview of the Riemann ζ-function with an eye to a proof of the functional equation that is non-standard and more accessible than those proofs readily available in modern texts. This is s survey note with the goal of a more elegant and transparent presentation of the salient features surrounding the functional equation for the ζ-function and the intimate connections with the Riem...
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The series is convergent when s is a complex number with <(s) > 1. Some special values of ζ(s) are well known, for example the values ζ(2) = π/6, ζ(4) = π/90, were obtained by Euler. In 1859, Riemann had the idea to define ζ(s) for all complex number s by analytic continuation. This continuation is very important in number theory and plays a central role in the study of the distribution of prim...
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Hilbert and Pólya put forward the idea that the zeros of the Riemann zeta function may have a spectral origin : the values of tn such that 1 2 + itn is a non trivial zero of ζ might be the eigenvalues of a self-adjoint operator. This would imply the Riemann Hypothesis. From the perspective of Physics one might go further and consider the possibility that the operator in question corresponds to ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00267-8