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Smallest absolute value of discriminant of a real (not necessarily totally real) algebraic number field of degree n.
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%I #5 Jun 30 2012 01:23:06

%S 5,23,275,1609,28037,184607

%N Smallest absolute value of discriminant of a real (not necessarily totally real) algebraic number field of degree n.

%C These values are important in Diophantine approximation theory and in the geometry of numbers. Krass (1985) proved that the n-dimensional simultaneous Diophantine approximation constant, gamma_n, must satisfy gamma_n >= (16/9)^floor(n/4) / sqrt(a_(n+1)). See web site for a continuation of probable values.

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 174-179.

%H Gerhard Niklasch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/dioph/niklasch.html">Smallest Discriminants of Number Fields</a>

%K hard,nonn

%O 2,1

%A _Robert G. Wilson v_, Jun 18 2002