כניסה

Root of Unity in Residue Rings of Algebraic Number Fields

Abstract:


This Talk is in the area of algebraic number theory. More specifically, we use explicit methods to determine the "roots of unity modulo M", namely, the solutions of equation x^n =1 in the ring O_K / M, where O_K is the ring of integers of a number field K. and M is an (integral) ideal of O_K.
The solutions are then applied to generalize a theorem of Bauer, counting the number of solutions to Pell equations modulo rational prime p and generalizing a theorem of Wolstenholme.

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