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Riemann-Siegel sums via stationary phase

Published online by Cambridge University Press:  17 April 2009

E. O. Tuck
E. O. Tuck
Affiliation:
Applied Mathematics Department, The University of Adelaide, Adelaide SA 5005, Australia
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A new representation is obtained for the Riemann ξ function, in the form of a series of integrals, multiplied by an exponential factor capturing the correct decay rate for large imaginary argument. Each term in this series then has a simple stationary-phase asymptote, the total agreeing with the Riemann-Siegel sum.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 325 - 328
Copyright
Copyright © Australian Mathematical Society 2005

References

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