A Parabolic Cylinder Function in the Riemann-Siegel Integral Formula

2015/12/03 by Gabcke, Wolfgang
#11M06 (Primary) #33E30 #44A20 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1512.01186

Abstract

We show that the two integrals in the Riemann-Siegel integral formula can be transformed into integral representations that contain the parabolic cylinder function U(a,z) as kernel function.

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