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- David H. Bailey, Richard E. Crandall
- Experimental Mathematics
- 2001

Bailey's work is supported by the Director, O ce of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC03-76SF00098. We propose a theory to explain random behavior for the digits in the expansions of fundamental mathematical constants. At the… (More)

- David H. Bailey, Richard E. Crandall
- Experimental Mathematics
- 2002

Pursuant to the authors’ previous chaotic-dynamical model for random digits of fundamental constants [5], we investigate a complementary, statistical picture in which pseudorandom number generators (PRNGs) are central. Some rigorous results are achieved: We establish b-normality for constants of the form ∑ i 1/(b ici) for certain sequences (mi), (ni) of… (More)

We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the… (More)

- David H. Bailey, Jonathan M. Borwein, +5 authors Carl Pomerance
- 2003

Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number #(|y|, N) of 1-bits in the expansion of |y| through bit position N… (More)

It is well known that Discrete Fourier Transform (DFT) techniques may be used to multiply large integers. We introduce the concept of Discrete Weighted Transforms (DWTs) which, in certain situations, substantially improve the speed of multiplication by obviating costly zero-padding of digits. In particular, when arithmetic is to be performed modulo Fermât… (More)

- Richard E. Crandall, Joe Buhler
- Experimental Mathematics
- 1994

AMS Subject Classi cation. Primary: 40A25, 40B05; Secondary: 11M99, 33E99.

- David H. Bailey, David Borwein, Jonathan M. Borwein, Richard E. Crandall
- Experimental Mathematics
- 2007

We apply experimental-mathematical principles to analyze integrals

Herein we present mathematical ideas for assessing the fractal character of distributions of brain synapses. Remarkably, laboratory data are now available in the form of actual 3-dimensional coordinates for millions of mouse-brain synapses (courtesy of Smithlab at Stanford Medical School). We analyze synapse datasets in regard to statistical moments and… (More)

- Joe Buhler, Richard E. Crandall, Reijo Ernvall, Tauno Metsänkylä, Amin Shokrollahi
- J. Symb. Comput.
- 2001

Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to 12 million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes (Shokrollahi, 1996). The latter idea reduces the problem to that of finding zeros of a polynomial over Fp of degree < (p− 1)/2… (More)