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Some news on bilinear decomposition of the Möbius function
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Authors : Ramaré, Olivier (Author of the conference)
CIRM (Publisher )
11A25 - "Arithmetic functions; related numbers; inversion formulas"
11N37 - Asymptotic results on arithmetic functions
11Y35 - Analytic computations
CIRM (Publisher )
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Abstract :
This talk presents some news on bilinear decompositions of the Möbius function. In particular, we will exhibit a family of such decompositions inherited from Motohashi's proof of the Hoheisel Theorem that leads to
$\sum_{n\leq X,(n,q)=1) }^{} \mu (n)e(na/q)\ll X\sqrt{q}/\varphi (q)$
for $q \leq X^{1/5}$ and any $a$ prime to $q$.
MSC Codes : $\sum_{n\leq X,(n,q)=1) }^{} \mu (n)e(na/q)\ll X\sqrt{q}/\varphi (q)$
for $q \leq X^{1/5}$ and any $a$ prime to $q$.
11A25 - "Arithmetic functions; related numbers; inversion formulas"
11N37 - Asymptotic results on arithmetic functions
11Y35 - Analytic computations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/10/14 Conference Date : 11/02/14 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:46:30 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-02-11_Ramare.mp4 
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Information on the Event
Event Title : Prime numbers : new perspectives / Nombres premiers : nouvelles perspectivesEvent Organizers : Dartyge, Cécile ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas Dates : 10/02/14 - 14/02/14 Event Year : 2014
Citation Data
DOI : 10.24350/CIRM.V.18606703Cite this video as: Ramaré, Olivier (2014). Some news on bilinear decomposition of the Möbius function. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18606703 URI : http://dx.doi.org/10.24350/CIRM.V.18606703 |
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