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SUMMARY:Problems in additive number theory: the Goldbach conjecture and it
 s variants
DTSTART:20260630T084500Z
DTEND:20260630T094500Z
DTSTAMP:20260707T001900Z
UID:indico-event-16909@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alessandra Migliaccio\n\nThe talk is devoted to pres
 enting some problems and techniques in additive theory\, a specific branch
  of analytic number theory. More precisely\, we begin with an overview of 
 the circle method - a fundamental tool introduced by Hardy\, Littlewood an
 d Ramanujan\; then\, we focus on its application to the Goldbach conjectur
 e\, and we underline the role of the so-called density in the study of rel
 ated additive problems - such as Vinogradov's theorem - compared to this o
 ne. In the second part of the seminar\, we explore our recent generalizati
 ons of two previous results: we first extend to polynomials computed at pr
 ime variables\, an estimate of M. Cantarini\, A. Gambini and A. Zaccagnini
  (2020) for the average number of representations of an integer as a sum o
 f prime powers. Eventually\, starting from the paper of K. Ikeda and A. I.
  Suriajaya (2025)\, we move to the arithmetic progressions\, and we find t
 he asymptotic behavior for the average number of representations of an int
 eger as a sum of two prime powers and of at least three primes\, over mult
 iples of a fixed integer. All of them are joint works with A. Zaccagnini.\
 n\nhttps://indico.math.cnrs.fr/event/16909/
LOCATION:Salle Fokko du Cloux (ICJ\, Université Lyon 1)
URL:https://indico.math.cnrs.fr/event/16909/
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