On a sum involving the Euler function

DOI10.1016/j.jnt.2019.01.006zbMath1454.11009arXiv1808.00188OpenAlexW2964033036WikidataQ128350326 ScholiaQ128350326MaRDI QIDQ5920209

Li-Xia Dai, Hao Pan, Randell Heyman, Olivier Bordellès, Igor E. Shparlinski

Publication date: 6 June 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.00188

zbMATH Keywords

Euler functioninteger partexponent pair

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (22)

Cardinality of a floor function set ⋮ Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski, 2 ⋮ On a sum involving small arithmetic functions ⋮ On certain sums of number theory ⋮ Three-dimensional exponential sums under constant perturbation ⋮ ON THE PRIMES IN FLOOR FUNCTION SETS ⋮ DISTRIBUTION OF r-FREE INTEGERS OVER A FLOOR FUNCTION SET ⋮ On fractional sums of the divisor functions ⋮ On a sum involving certain arithmetic functions on Piatetski-Shapiro and Beatty sequences ⋮ On general sums involving the floor function with applications to \(k\)-free numbers ⋮ On a sum involving small arithmetic function and the integral part function ⋮ On a variant of the prime number theorem ⋮ On a sum involving certain arithmetic functions and the integral part function ⋮ CORRECTION TO ‘NOTE ON SUMS INVOLVING THE EULER FUNCTION’ ⋮ Primes in floor function sets ⋮ On a sum involving the sum-of-divisors function ⋮ On a sum involving the Mangoldt function ⋮ On a sum involving the Euler function ⋮ On a sum involving the divisor function ⋮ NOTE ON SUMS INVOLVING THE EULER FUNCTION ⋮ A variant of the prime number theorem ⋮ On a generalisation of Bordellès-Dai-Heyman-Pan-Shparlinski's conjecture

Cites Work

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• PRIMES IN BEATTY SEQUENCES IN SHORT INTERVALS
• Decoupling, exponential sums and the Riemann zeta function
• The Burgess inequality and the least kth power non-residue
• Explicit averages of non-negative multiplicative functions: going beyond the main term
• The sum of digits of \lfloor n^c\rfloor
• Squares in Piatetski-Shapiro sequences
• Short interval results for certain arithmetic functions
• Piatetski-Shapiro sequences
• SUMS OF MULTIPLICATIVE FUNCTIONS OVER A BEATTY SEQUENCE
• Arithmetic functions on Beatty sequences
• Some extremal functions in Fourier analysis
• CHARACTER SUMS WITH PIATETSKI-SHAPIRO SEQUENCES
• Friable values of Piatetski-Shapiro sequences

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