p-adic quotient sets: diagonal forms

نویسندگان

چکیده

For a set of integers A, we consider \(R(A)=\{a/b: a, b\in b\ne 0\}\). It is an open problem to study the denseness R(A) in p-adic numbers when A nonzero values attained by integral form. This has been answered for quadratic forms. Very recently, Antony and Barman have studied this diagonal binary cubic forms \(ax^3+by^3\), where b are integers. In article, We extend their results \(ax^n+by^n\) all \(n\ge 3\). also quotients degree 3\), \(\gcd (n,p(p-1))=1\).

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ژورنال

عنوان ژورنال: Archiv der Mathematik

سال: 2022

ISSN: ['0003-889X', '1420-8938']

DOI: https://doi.org/10.1007/s00013-022-01785-3