The Riesz Energy of the N-th Roots of Unity: an Asymptotic Expansion for Large N
نویسندگان
چکیده
We derive the complete asymptotic expansion in terms of powers of N for the Riesz s-energy of N equally spaced points on the unit circle as N →∞. For s ≥ −2, such points form optimal energy N -point configurations with respect to the Riesz potential 1/r, s 6= 0, where r is the Euclidean distance between points. By analytic continuation we deduce the expansion for all complex values of s. The Riemann zeta function plays an essential role in this asymptotic expansion.
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