Almost universality of a sum of norms
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Publication:290925
DOI10.32917/HMJ/1459525930zbMATH Open1415.11068arXiv1302.2457OpenAlexW2963144029WikidataQ128866441 ScholiaQ128866441MaRDI QIDQ290925
Publication date: 3 June 2016
Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1302.2457
Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Representation problems (11D85) Multiplicative and norm form equations (11D57)
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