Infinite sets of primes, admitting diophantine representations in eight variables |
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Authors: | M A Vsemirnov |
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Abstract: | The existence of infinite sets of primes which can be repesented as the sets of positive values of some polynomials in a small
number of variables is discussed. (All variables range over positive integers.) It is proved (noneffectively) that there exists
such a set, which has a representation with eight variables. This number of variables is smaller than in the best universal
construction known today, which is ten. Also, some improvements of well-known technical lemmas are given. Bibliography: 20
titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 36–48.
Translated by M. A. Vsemirnov. |
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