On primes in special sequences with applications to Carmichael numbers
Abstract
By involving some exponential sums related to (n) in arithmetic progression, we can obtain some new results for von Mangoldt function over nonhomogeneous Beatty sequences in arithmetic progressions, which improve some recent results of Banks-Yeager unconditionally. On the other hand, we also considered the primes over Piatetski-Shapiro sequences in arithmetic progressions, which gives a continuous improvement of the results of BBB. These results can be used to improve some results related to the Carmichael numbers.
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