A Diophantine Inequality Involving Mixed Powers of Primes with a Specific Type

Tatiana L. Todorova and Atanaska Georgieva ()
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Tatiana L. Todorova: Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1000 Sofia, Bulgaria
Atanaska Georgieva: Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

Mathematics, 2025, vol. 13, issue 19, 1-21

Abstract: Let λ 1 , λ 2 , λ 3 be nonzero real numbers, not all of the same sign; let λ 1 / λ 2 be irrational; and let η be any real number. We investigate the solvability of the inequality | λ 1 p 1 + λ 2 p 2 + λ 3 p 3 2 + η | < ( max p j ) − 1 / 12 + θ , θ > 0 in the prime variables p 1 , p 2 , and p 3 . We require that p 1 + 2 and p 2 + 2 have no more than 20 prime factors, while p 3 + 2 has no more than 42 prime factors.

Keywords: Rosser’s weights; vector sieve; circle method; almost primes; diophantine inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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