• specialization theorems

    From nobody@nowhere.invalid@21:1/5 to clicliclic@freenet.de on Thu Sep 10 19:23:03 2020
    "clicliclic@freenet.de" schrieb:

    Still nothing official is to be found on the internet of Masser and
    Zannier's work that lead to counterexamples to a theorem by James H. Davenport: Some parametrized algebraic functions not identically
    integrable can actually be integrated for infinitely many parameter
    values.

    Nothing official, that is, apart from David Masser's feature article "Integration in elementary terms" in the LMS Newsletter (Newsletter
    London Math. Soc. 473 (2017), 30-36), made available here:

    <https://webusers.imj-prg.fr/~jan.nekovar/co/ter/int.pdf>

    [...]


    Just noticed that an official preprint has become available at:

    <https://dmi.unibas.ch/de/personen/david-masser/publikationen/>

    One quick remark: The antiderivatives of integrals (14.4) and (21.11)
    could be simplified substantially: their numerators and denominators in
    essence are squares. As written, the logarithms look more impressive
    though! ... Hmmm.

    Martin.

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Tue Oct 26 00:37:42 2021
    They published it. https://www.intlpress.com/site/pub/pages/journals/items/acta/content/vols/0225/0002/a002/

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  • From =?UTF-8?B?0JLQsNC70LXRgNC40Lkg0JfQs@21:1/5 to All on Sat Feb 5 16:01:22 2022
    вторник, 26 октября 2021 г. в 10:37:44 UTC+3, Валерий Заподовников:
    They published it. https://www.intlpress.com/site/pub/pages/journals/items/acta/content/vols/0225/0002/a002/

    Can we discuss this paper? I mean they refuted Davenport's theorem
    there, modified it to be true and even gave insane amount of different integrals, including some criticism/typos of Greenhill book! Very nice.

    And looks like it has some implications on Risch algorithm.

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