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ifm is odd then the only fixed point isa= 0 so there are (md−1)/2+1 = (md+1)/2 representatives

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ERRATA:

ENUMERATION OF TOTALLY REAL NUMBER FIELDS OF BOUNDED ROOT DISCRIMINANT

JOHN VOIGHT

This note gives some errata for the article Enumeration of totally real number fields of bounded root discriminant [1].

(1) Page 9, paragraph 3, line 2, “2dor dmd/2epossibilities”: This is not quite correct. There are certainlyO(md) possibilities, and this does not affect any other statement in the paper. (One just computes representatives modulo

±1 for ZE/mZE: if m = 2 then the action is trivial, and there are 2d representatives; ifm is odd then the only fixed point isa= 0 so there are (md−1)/2+1 = (md+1)/2 representatives; ifmis even then the fixed points are the 2d elements of (m/2)·ZE/mZE, so there are (md−2d)/2 + 2d = md/2 + 2d−1. But this does not really make any difference.)

References

[1] John Voight,Enumeration of totally real number fields of bounded root discriminant, Algo- rithmic number theory (ANTS VIII, Banff, 2008), eds. Alfred van der Poorten and Andreas Stein, Lecture Notes in Comp. Sci., vol. 5011, Springer, Berlin, 2008, 268–281.

Date: May 27, 2014.

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