Journal of Mathematical Techniques and Computational Mathematics(JMTCM)

Department of Mathematics, University of Liverpool, M&O Building, Peach St, Liverpool L69 7ZL, UK

Publications

• Research Article   
  A Computational Algorithm For The Hardy Function Z(t), Utilizing Sub-Se-quences of Generalized Cubic Gauss Sums, With An Overall Operational Complexity O((t⁄εt)[0.25, 0.3]{log(t)}2+o(1)) FOR ∈[1023−35]
  Author(s): D. M. Lewis* and A. R. Brereton
  
  In 2011 G. A. Hiary devised a computational algorithm for the Hardy function �?�(�?�), requiring just �??(�?�1/3{�??�??�??(�?�)}�??) operations. This compares to �??  operations necessary for computing �?�(�?�) using the classical Riemann-Siegel formula. The methodology involved the sub-division of the Riemann-Siegel formula into sequences of quadratic Gauss/exponential sums of various lengths �?�. Such sums can be computed rapidly, in �??(�??�??�??(�?�)) operations, using standard recursive schemes. More recently, the principal author developed a similar algorithm with an �??((�?�⁄ �?�)1⁄3{�??�??�??(�?�)}2) operational count, accurate to �?� in the relative error. Although constructively analogous, the sub-division into quadratic sums was applied to a different asymptotic formula f.. Read More»
  

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