arXiv subjects

Pin-Hung Kao

Publications and source records attributed to Pin-Hung Kao.

2 recordsLinked to original sources

arXiv2016

Almost-Prime Polynomials with Prime Arguments

We improve Irving's method of the double-sieve by using the DHR sieve. By extending the upper and lower sieve functions into their respective non-elementary ranges, we are able to make improvements on the previous records on the number of prime factors of irreducible polynomials at prime arguments. In particular, we prove that irreducible quadratics over $\mathbb{Z}$ satisfying necessary local conditions are $P_4$ infinitely often.

math.NT↗

arXiv2012

Betti Tables of Reducible Algebraic Curves

We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses. We also give explicit formulas for the entries of the Betti tables for all curves of genus zero and one. Last, we give formulas for the graded Betti numbers for a class of curves of higher genus.

math.AG↗