The WKB method used in the number theory

Speaker(s)

Henryk Żołądek

Affiliation

Uniwersytet Warszawski

Date

Feb. 26, 2010, 10:15 a.m.

Room

room 5840

Seminar

Seminar of Dynamical Systems Group

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Some generating functions for so-called multiple zeta values are directly related with some solutions to linear differential equations with meromorphic coefficients. For example, the function f₃(x) = 1 - ζ(3)x³ + ζ(3,3)x⁶ - ...  is equal to the value at t = 1 of the hypergeometric function F(-x, εx, ε^-1x; 1, 1; t) (where ε = e^iπ/3). Together with M. Zakrzewski we applied asymptotic analysis as x→∞ (of WKB type) for the hypergeometric equations related with ζ(2) and ζ(3). We proved that the corresponding generating functions satisfy linear differential equations of Bessel type.

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