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A ternary Diophantine inequality over primes

Volume 162 / 2014

Roger Baker, Andreas Weingartner Acta Arithmetica 162 (2014), 159-196 MSC: Primary 11N36; Secondary 11L20, 11P55. DOI: 10.4064/aa162-2-3


Let $1< c< 10/9$. For large real numbers $R>0$, and a small constant $\eta >0$, the inequality $$ | p_1^c+p_2^c+p_3^c - R| < R^{-\eta } $$ holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].


  • Roger BakerDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, U.S.A.
  • Andreas WeingartnerDepartment of Mathematics
    Southern Utah University
    Cedar City, UT 84720, U.S.A.

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