Disjointness of the Möbius Transformation and Möbius Function

Abdalaoui, El Houcein El; Shparlinski, Igor E.

doi:10.1007/s40687-019-0180-6

Cited by 2 publications

(14 citation statements)

References 51 publications

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“…Theorem 2.6. For any fixed integer 𝑎, and 𝑘 ≥ 2, we have 𝖧 𝑎,𝜅 𝑘 (𝑀) ≤ 𝑀 1∕2+𝛾+𝑜(1) + 𝑀 1∕2+1∕(2𝑘)+𝑜 (1) .…”

Section: New Results In the Horizontal Aspectmentioning

confidence: 99%

“…are small compared to their trivial bound 𝑁𝑚 𝑜 (1) , which follows from (1.1), for some "interesting" (bounded) arithmetic sequence 𝑏 𝑛 , 𝑛 = 1, … , 𝑁, and some integer shifts 0 ≤ ℎ 1 < … < ℎ 𝑠 < 𝑞, see Lemma 3.3, due to Fouvry, Kowalski, and Michel [22,Corollary 1.6], for one of such results.…”

Section: Set-upmentioning

confidence: 98%

“…are small compared to their trivial bound 𝑀 1+𝑜 (1) , which follows from (1.1), for some "interesting" (bounded) sequence 𝑎 𝑚 , 𝑚 = 1, … , 𝑀, and some integer shifts 0 ≤ ℎ 1 < … < ℎ 𝑠 ; (2) vertical randomness, that is, one aims to show that the sums of the types…”

Section: Set-upmentioning

confidence: 99%

“…The choice 𝑇 = 0.5(𝑞𝑀) 2∕3 (which due to (3.2) ensures that 1 ≤ 𝑇 ≤ 𝑀∕2, as required) gives the bound (1) .…”

Section: Sums Of Kloosterman Sums In the Horizontal Aspectmentioning

confidence: 99%

“…Since Kloosterman sums depend on two parameters 𝑎 and 𝑚, following standard terminology, one can study (1) horizontal randomness, that is, one aims to show that the sums of the types 𝑀 ∑ 𝑚=1 𝑎 𝑚  𝑚 (𝑎) and…”

Section: Set-upmentioning

confidence: 99%

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