Let be any real prime of a number field , and write for the corresponding real embedding of . We say two elements are multiplicatively congruent mod if the real numbers and are either both positive or both negative.
Now let be a finite prime of , and write for the localization of the ring of integers of at . For any natural number , we say and are multiplicatively congruent mod if they are members of the same coset of the subgroup of the multiplicative group of .
If is any modulus for , with factorization
then we say and are multiplicatively congruent mod if they are multiplicatively congruent mod for every prime appearing in the factorization of .
Multiplicative congruence of and mod is commonly denoted using the notation
|Date of creation||2013-03-22 12:50:16|
|Last modified on||2013-03-22 12:50:16|
|Last modified by||djao (24)|