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Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality
holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].
Roger Baker, and Andreas Weingartner. "A ternary Diophantine inequality over primes." Acta Arithmetica 162.2 (2014): 159-196. <http://eudml.org/doc/279105>.
@article{RogerBaker2014, abstract = {Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality
$|p₁^c+p₂^c+p₃^c - R| < R^\{-η\}$
holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].}, author = {Roger Baker, Andreas Weingartner}, journal = {Acta Arithmetica}, keywords = {diophantine inequalities; exponential sums with monomials; alternative sieve; Davenport-Heilbronn method}, language = {eng}, number = {2}, pages = {159-196}, title = {A ternary Diophantine inequality over primes}, url = {http://eudml.org/doc/279105}, volume = {162}, year = {2014}, }
TY - JOUR AU - Roger Baker AU - Andreas Weingartner TI - A ternary Diophantine inequality over primes JO - Acta Arithmetica PY - 2014 VL - 162 IS - 2 SP - 159 EP - 196 AB - Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality
$|p₁^c+p₂^c+p₃^c - R| < R^{-η}$
holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)]. LA - eng KW - diophantine inequalities; exponential sums with monomials; alternative sieve; Davenport-Heilbronn method UR - http://eudml.org/doc/279105 ER -