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Cyclotomic coefficients: gaps and jumps. (English) Zbl 1405.11032

Summary: We improve several recent results by Hong, Lee, Lee and Park [H. Hong et al., J. Number Theory 132, No. 10, 2297–2315 (2012; Zbl 1273.11051)] on gaps and B. Bzdęga [Acta Arith. 163, No. 3, 203–213 (2014; Zbl 1307.11032)] on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have never been used in this area.

MSC:

11C08 Polynomials in number theory
11B83 Special sequences and polynomials
11L07 Estimates on exponential sums
11N25 Distribution of integers with specified multiplicative constraints
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References:

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