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Approximating the Riemann Zeta and Related Functions

In: Progress in Approximation Theory and Applicable Complex Analysis

Author

Listed:
  • Frank Stenger

    (School of Computing, University of Utah)

Abstract

In this chapter we study the well-known function G, as well as some other functions that have the same zeros as the Riemann zeta function ζ(z) in the critical strip. To this end, we first derive a Fourier series expansion of G. Next, we use asymptotic methods to derive another function which also has the same zeros in the critical strip as ζ(z), but which lacks the extreme oscillatory behavior and extreme amplitude values that ζ(z) possesses, and which is therefore more suitable for computational purposes.

Suggested Citation

  • Frank Stenger, 2017. "Approximating the Riemann Zeta and Related Functions," Springer Optimization and Its Applications, in: Narendra Kumar Govil & Ram Mohapatra & Mohammed A. Qazi & Gerhard Schmeisser (ed.), Progress in Approximation Theory and Applicable Complex Analysis, pages 363-373, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-49242-1_17
    DOI: 10.1007/978-3-319-49242-1_17
    as

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