Weil numbers in prime cyclotomic fields, by Kiran S. Kedlaya
For m a positive integer,
an m-Weil number is an algebraic integer with squared complex norm
m under every embedding into the complex numbers. We conjecture that
for m fixed, the set of m-Weil numbers in the union
of all cyclotomic fields can be obtained from some finite set by multiplication
by roots of unity. We prove the analogous but weaker assertion for the
set of m-Weil numbers in the union of all prime cyclotomic fields.
Kiran S. Kedlaya <kedlaya@math.berkeley.edu>