A ternary Diophantine inequality over primes
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)].
Primes in arithmetic progressions to spaced moduli
Primitive lattice points in planar domains
Kloosterman sums with prime variable
Gaps between primes in Beatty sequences
We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).
Sparsely totient numbers
Piatetski-Shapiro sequences
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