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SUMMARY:Sinai Robins (Universidade de  São Paulo)
DTSTART:20220629T160000Z
DTEND:20220629T170000Z
DTSTAMP:20260423T021251Z
UID:HAeS/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/35/">Th
 e covariogram and extensions of the Bombieri-Siegel formula</a>\nby Sinai 
 Robins (Universidade de  São Paulo) as part of Harmonic analysis e-semina
 rs\n\n\nAbstract\nWe extend a formula of C. L. Siegel in the geometry of n
 umbers\, allowing the body to contain an arbitrary number of interior latt
 ice points. Our extension involves a lattice sum of the cross covariogram 
 for any two bounded sets $A\, B\\subseteq \\mathbb R^d$\, and turns out to
  also extend a\nresult of E. Bombieri. We begin with a new variation of th
 e Poisson summation formula\, which may be of independent interest. One of
  the consequences of these results is a new characterization of multitilin
 gs of Euclidean space by translations\, which is an application of Bombier
 i’s identity and of our extension of it. Some classical results\, such a
 s Van der Corput’s inequality\, and Hardy’s identity for the Gauss cir
 cle problem\, also follow as corollaries. This is joint work with Michel F
 aleiros Martins.\n
LOCATION:https://researchseminars.org/talk/HAeS/35/
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