Rational approximations to the zeta function
Copyright policy )Rational approximations to the zeta function
This article describes a sequence of rational functions which converges locally uniformly to ζ . The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that are on the face of it very simple. As a consequence, the Riemann hypothesis can be restated as what looks like a rather conventional spectral problem but which is related to the one found by Connes and by Berry and Keating. However the point here is that the rational approximations look to be susceptible of quantitative estimation.
- University of Warwick United Kingdom
number theory, rational function, Mathematics - Number Theory, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Number Theory (math.NT), QA, approximation, zeta function
number theory, rational function, Mathematics - Number Theory, \(\zeta (s)\) and \(L(s, \chi)\), FOS: Mathematics, Number Theory (math.NT), QA, approximation, zeta function
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