2013/02/11 by Jeongho Park, Park, Jeongho
Mathematics · #11D57 #11D85 #FOS: Mathematics #Number Theory (math.NT) #Primary 11P05 #Secondary 11P55 #math.NT #msc:11D57 #msc:11D85 #msc:11P05 #msc:11P55
paper · pdf · doi:10.48550/arxiv.1302.2457
arxiv created 2015/11/26 · arxiv updated 2015/11/30
In this paper the author considers a particular type of polynomials with integer coefficients, consisting of a perfect power and two norm forms of abelian number fields with coprime discriminants. It is shown that such a polynomial represents every natural number with only finitely many exceptions. The circle method is used, and the local class field theory plays a central role in estimating the singular series.