While the previous proof had relied on many different methods, the new version relied almost exclusively on the behavior of cyclotomic polynomials over finite fields.
42.
The cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's last theorem.
43.
These characters and their associated L-functions are now understood to be strictly related to complex multiplication, as the Dirichlet characters are to cyclotomic fields.
44.
*PM : the cyclotomic units are algebraic units, id = 5657-- WP guess : the cyclotomic units are algebraic units-- Status:
45.
*PM : the cyclotomic units are algebraic units, id = 5657-- WP guess : the cyclotomic units are algebraic units-- Status:
46.
The general theory of Gauss sums was developed in the early nineteenth century, with the use of Jacobi sums and their prime decomposition in cyclotomic fields.
47.
Note that, contrary to first appearances, " not " all coefficients of all cyclotomic polynomials are 0, 1, or " 1.
48.
This number lies in the " n "-th cyclotomic field & mdash; and in fact in its real subfield, which is a dimension
49.
Iwasawa is perhaps best known for introducing what is now called Iwasawa theory, which developed from researches on cyclotomic fields from the later parts of the 1950s.
50.
Then " G " has a canonical cyclotomic character ? given by its action on the " p " th power roots of unity.
