On primes in special sequences with applications to Carmichael numbers

2022/07/06 by Wei Zhang, Zhang, Wei
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2207.02378

openalex publication_date 2022/07/06 · openalex created_date 2022/07/09 · openalex updated_date 2026/07/28

Abstract

By involving some exponential sums related to Λ(n) in arithmetic progression, we can obtain some new results for von Mangoldt function over \bf 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 \citeBBB. These results can be used to improve some results related to the Carmichael numbers.

Related

• Arithmetic progressions of Carmichael numbers in a reduced residue class
• Piatetski-Shapiro sequences
• Gaps between Primes in Beatty Sequences
• Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors
• On Generalized Carmichael Numbers