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UID:8491@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250116T170000
DTEND;TZID=Europe/Paris:20250116T180000
DTSTAMP:20241128T095326Z
URL:https://www.i2m.univ-amu.fr/evenements/arithmetic-from-elementary-stat
 ements-to-complex-tools/
SUMMARY:Jeremy Dousselin (Université de Lorraine): Arithmetic: from elemen
 tary statements to complex tools
DESCRIPTION:Jeremy Dousselin: \n\nAbstract : In 1896\, Hadamard and de La V
 allée Poussin proved the famous prime number theorem\, which gives an asy
 mptotic formula in $x$ for the number of prime numbers $p\\leq x$. Their p
 roof heavily relies on complex analysis. Hardy\, along with some other ma
 thematicians in the 20\\textsuperscript{th} century\, wondered whether or 
 not some theorems could only be proved using integers/real numbers/complex
  numbers. Hardy believed that the prime number theorem was one of those th
 at required the use of complex numbers. This turned out not to be the case
 \, as was discovered when Selberg and Erdös proved the prime number theor
 em using only elementary means. That being said\, why is it natural to con
 sider complex numbers when proving some arithmetic statements?\n\nThe aim 
 of this talk is to outline the ideas that link prime numbers to deep tools
  such as exponential sums and the residue theorem. Of course\, we will hav
 e to take some time to see how the Riemann Hypothesis relates to all these
  facts.\n\n\n\n&nbsp\;\n\n\n\nLe séminaire des doctorant⋅es de l'I2M et
  du CPT à Luminy regroupe chaque semaine les doctorant⋅es du site autou
 r d'un exposé plus ou moins (in)formel\, dans un cadre convivial. Il est 
 évidemment ouvert aux étudiant⋅es de master et aux doctorant⋅es d'au
 tres laboratoires.\n\nPour le moment\, le séminaire a lieu dans la salle 
 500-504b du TPR2\, au 5ème étage.
CATEGORIES:Séminaire,Rencontres doctorant⋅es I2M-CPT
LOCATION:Luminy - salle 500-504b\, Aix-marseille université-faculté des s
 ciences\, campus Luminy\, Marseille\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Aix-marseille université-f
 aculté des sciences\, campus Luminy\, Marseille\, France;X-APPLE-RADIUS=1
 00;X-TITLE=Luminy - salle 500-504b:geo:0,0
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TZID:Europe/Paris
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