Asks and Acknowledgements

Asks

MT is a free ware. Use as you like. When you use the code, I wish you to let me know how and what purpose you use it, how is the result, and a proper reference to your result, if you can, preferably to m-mat @ math.sci.hiroshima-u.ac.jp (remove two spaces by hand). If possible, let me know a link to your results.
If you have any improvement, problems, applications of MT (e.g. other implementation, assembly language, non-uniform random variates, etc.), and you allow us to link them to this home page, please let me know.
MT uses results of pure abstract mathematics, in particular a classical number theory developed 50-100 years ago, and at that time they were not considered to be useful to the science. These days, pure abstract mathematics are considered to be redundant even in universities, and mathematics departments tend to be closed or changed into informatics. We don't think this is a right way. Pure mathematics shows "unexpected unreasonable effectiveness" in many areas of the science, although its effectiveness is not so easily percepted by the society, compared to other branches of science. We are glad if you take it into consideration that the present society is supported by mathematics developped hundreds years ago, and the next generation might be supported by the modern mathematics which might seem to be too abstract to utilize in the society, just right now.

Acknowledgements

The idea of Twisting in MT comes from the discussion with Prof. Nobuo Yoneda who left us in Apr. 1996. The paper is dedicated to his memory.

A previous ancestor of MT, Twisted GFSR is a joint work of Matsumoto and Y. Kurita.

MT is a descent of F2 linear generators and heavily depends on the researches by Professors M. Fushimi, S. Tezuka, P. Lecuyer, R. Couture, H. Niederreiter, and many many other researchers whose names we omit here.

The research of MT is helped by Dept. of Math of Keio University, RIMS at Kyoto University, CRM of Montreal University, Max-Planck-Institute for Mathematics, Salzburg University, and many other institutes, and supported by a Monbusho grant.

MT uses many existing ideas. In particular, we are thankful to the following persons.
N. Yoneda, P. L'Ecuyer, R. Couture, H. Niederreiter, P. Hellekalek, M. Fushimi, S. Tezuka, Y. Kurita, D. Knuth, H. Leeb, S. Wegenkittl, T. Cooper, M. Rieffel, H. Enomoto, and many many persons who gave us valuable comments, including the users of TT800, a previous twisted generator.