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This article is cited in 11 scientific papers (total in 11 papers)
Primes in Special Intervals and Additive Problems with Such Numbers
M. E. Changa Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We study primes in a special set $E$ which is naturally described by the fractional part of $p^a$, where $a<1$ is a noninteger. An asymptotic formula with power lowering in the remainder of the trigonometric sum over primes from the set $E$ is obtained. We study several applications of this result to problems of the distribution of primes from $E$ in arithmetic progressions and to additive problems with primes from $E$.
Received: 25.06.2002
Citation:
M. E. Changa, “Primes in Special Intervals and Additive Problems with Such Numbers”, Mat. Zametki, 73:3 (2003), 423–436; Math. Notes, 73:3 (2003), 389–401
Linking options:
https://www.mathnet.ru/eng/mzm192https://doi.org/10.4213/mzm192 https://www.mathnet.ru/eng/mzm/v73/i3/p423
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Abstract page: | 438 | Full-text PDF : | 176 | References: | 39 | First page: | 1 |
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