
TL;DR
This paper investigates bounds related to products in modular arithmetic constrained by Beatty sequences, using advanced exponential sum techniques and autocorrelation bounds, contributing new results under specific conditions on the sequence parameters.
Contribution
It provides new bounds for solutions to modular equations involving Beatty sequences, employing a method by Banks and Shparlinski and adapting Kloosterman sum techniques.
Findings
Bounds for $ ext{max}igrace{m, ilde{m}igrace}$ under given modular and sequence conditions
Average bounds for discrete autocorrelation of specific exponential sequences
Application of advanced exponential sum methods to Beatty sequence problems
Abstract
Bounds for subject to , prime, indivisible by , and belonging to some fixed Beatty sequence are obtained, assuming certain conditions on . The proof uses a method due to Banks and Shparlinski. As an intermediate step, bounds for the discrete periodic autocorrelation of the finite sequence on average are obtained, where and . The latter is accomplished by adapting a method due to Kloosterman.
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