Polynomial Isometries of p-adic Integers
Mentor:Zair Ibragimov, Assistant Professor, California State University Fullerton
In this talk I will discuss polynomial isometries of p-adic integers. The p-adic integers is the completion of the usual integers with respect to the p-adic norm. By the recent work of Professor Martial Aufranc the study of polynomial isometries of the p-adic integers can be reduced to studying polynomial bijections of Fp, the field of p elements. In this talk I will give a characterization of such bijections for p=3,5 and 7 and I will also give a general characterization of all polynomial bijections of Fp for all prime numbers p.