题目：Counting Roots for Polynomials Modulo Prime Powers

报告人： Qi Cheng （University of Oklahoma）

Abstract : Suppose $p$ is a prime, $t$ is a positive integer, and

$f /in /Z[x]$ is a univariate polynomial of degree $d$ with coefficients

of absolute value $< p^t$. We show that for any {/em fixed} $t$, we can

compute the number of roots in $/Z/(p^t)$ of $f$ in deterministic

time $(d/log p)^{o(1)}$. This fixed parameter tractability appears

to be new for $t /geq 3$. A consequence for arithmetic geometry is that

we can efficiently compute the Igusa zeta functions $Z$, for univariate

polynomials, assuming the degree of $Z$ is fixed.

简介：

Dr. Qi Cheng is the Williams Companies Foundation Presidential Professor in the School of Computer Science at the University of Oklahoma. His main research areas are in theoretical computer science, cryptography, coding theory, computational number theory and molecular computing. He obtained the B.S. degree from Nankai University in 1992, the M.S. degree from Fudan University in 1995, and the Ph.D. degree in computer science from the University of Southern California in 2001.  He is a recipient of the NSF CAREER Award in 2003, and a recipient of the distinguished paper award of ISSAC 2013.

时间：7月6日（周五）下午15:30-16:30

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