An alternative to Riemann-Siegel type formulas

Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable square-root of the analytic conductor complexity, up to logarithmic loss, and have an explicit remainder term that is easy to control. The formula for zeta yields a convexity bound of the same strength as that from the Riemann-Siegel formula, up to a constant factor. Practical parameter choices are discussed.Comment: 16 page

Fast methods to compute the Riemann zeta function

The Riemann zeta function on the critical line can be computed using a straightforward application of the Riemann-Siegel formula, Sch\"onhage's method, or Heath-Brown's method. The complexities of these methods have exponents 1/2, 3/8 (=0.375), and 1/3 respectively. In this paper, 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 employs an algorithm, developed in this paper, to compute cubic exponential sums. Its complexity has exponent 4/13 (approximately, 0.307).Comment: Presentation simplifie

Enhanced Pilot-Based Spectrum Sensing Algorithm

In this paper, we develop an enhanced pilot-based spectrum sensing algorithm for cognitive radio. Unlike conventional pilot-based detectors which merely detect the presence of pilot signals, the proposed detector also utilizes the presence of the signal that carries the actual information. We analytically compare the performance of the proposed detector with the conventional one, and we show that the detection performance is significantly improved.Comment: 4 pages, 2 figures; published in Proc. IEEE Biennial Symps. on Commun. (QBSC'14), June 201

Mapping erosion-corrosion of carbon steel in oil-water solutions : Effect of velocity and applied potential

In this study, the combined effects of erosion and corrosion on carbon steel were investigated in three environments containing crude oil, reservoir water, and a mixture of both solutions at a range of applied potentials, velocities and impact angle. The results indicate that the corrosion contribution was augmented with an increase in the percentage of reservoir water. Both the erosion and corrosion contributions increased with impact velocity for all three environments. Following exposure of the carbon steel in the crude oil, the extent of the erosion was greater than that of corrosion, whilst in the reservoir water, the erosion and corrosion contributions were similar. Mechanisms of erosion-corrosion were proposed based on the change in erosion behaviour at various impact angles and applied potentials in the various environments. Erosion-corrosion maps were constructed based on the results, showing the change in mechanisms and wastage rates as a function of impact velocity and applied potential at various impact angles