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SUMMARY:Vesselin Dimitrov (Caltech)
DTSTART:20261006T193000Z
DTEND:20261006T203000Z
DTSTAMP:20261022T233905Z
UID:BC-MIT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/35/">
 Arithmetic Gevrey series and the nearest integer to $\\log{n}$</a>\nby Ves
 selin Dimitrov (Caltech) as part of BC-MIT number theory seminar\n\nLectur
 e held in 2-449 at MIT.\n\nAbstract\nI will report on the continued joint 
 project with Calegari and Tang on arithmetic holonomy bounds\, this time i
 n the broader context of Gevrey series. \n\nWe give an extension of Andre'
 s algebraicity criterion to the arithmetic Gevrey class\, which turns out 
 to contain the Hermite-Lindemann theorem directly as a special case. Anoth
 er application solves the following problem first raised by Mahler: We pro
 ve that for all integers $n > 1$\, the nearest integer distance to $\\log{
 n}$ is bounded below by some universal polynomial in $1/n$. \n\nIn the lan
 guage of the theory of linear forms in logarithms\, this supplies precisel
 y the Waldschmidt parameter feature (which has only been proved for homoge
 neous linear forms with rational coefficients) in the inhomogeneous case o
 f linear forms in logarithms on $\\mathbb{G}_a \\times \\mathbb{G}_m$.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/35/
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