Galois Groups of p-Adic Polynomials of Fixed Degree
نویسندگان
چکیده
Given an integer n and a group G we estimate the probability that a random, monic, degree n, p-adic polynomial has Galois group isomorphic to G. A comparison is made with classic results concerning Galois groups of random, monic, degree n polynomials with integer coefficients. We conclude by analyzing the probability that a random, monic, degree n polynomial in Z[x] has these properties: its Galois group is isomorphic to Sn; that a given prime p > n2 + n is unramified in its splitting field, K; that the prime p lies under a prime of K with Artin symbol in a prescribed conjugacy class.
منابع مشابه
Saturday, November 7
9:00 Galois Groups of Random p-adic Polynomials Benjamin Weiss The space of fixed degree polynomials with p-adic coefficients has a natural probability distribution. Each polynomial also has an associated group which is the Galois group of its splitting field. We will discuss the induced distribution on groups, and derive results for the limiting distribution as p grows. Time permitting, we wil...
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