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- W2138245810 abstract "The Riemann zeta function on the critical line can be computed using a straightforward application of the Riemann-Siegel formula, Schonhage's method, or Heath-Brown's method. The complexities of these methods have exponents 1/2, 3/8, and 1/3 respectively. In this article, three new fast and potentially practical methods to compute zeta are presented. One method is very simple. Its complexity has exponent 2/5. A second method relies on this author's algorithm to compute quadratic exponential sums. Its complexity has exponent 1/3. The third method, which is our main result, employs an algorithm developed here to compute cubic exponential sums with a small cubic coecient. Its complexity has exponent 4/13 (approximately, 0.307)." @default.
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- W2138245810 date "2011-09-01" @default.
- W2138245810 modified "2023-09-27" @default.
- W2138245810 title "Fast methods to compute the Riemann zeta function" @default.
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- W2138245810 doi "https://doi.org/10.4007/annals.2011.174.2.4" @default.
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