skip to main content

Search for: All records

Creators/Authors contains: "Walker, Robert M."

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Until recently, the only known method of finding the roots of polynomials over prime power rings, other than fields, was brute force. One reason for this is the lack of a division algorithm, obstructing the use of greatest common divisors. Fix a prime integer p and f in (Z/pnZ)[x] any nonzero polynomial of degree d whose coefficients are not all divisible by p. For the case n=2, we prove a new efficient algorithm to count the roots of f in Z/p2Z within time (d+size(f)+log p),2+o(1), based on a formula conjectured by Cheng, Gao, Rojas, and Wan. 
    more » « less