[seqfan] Re: Reference Help?

[Jean-Paul Allouche]

Hi

I found a 2017 paper of Coster where there is an email for him. May be the
email is still valid?
see http://www.nieuwarchief.nl/serie5/pdf/naw5-2017-18-3-205.pdf

Also his PhD advisers were Bob Tijdeman and Fritz Beukers whose emails are
easy to find

best wishes
jean-paul



Le sam. 3 juin 2023, 05:05, brad klee via SeqFan <seqfan at list.seqfan.eu> a
écrit :

> Hiya seqfans,
>
> It was recently brought to my attention that a few sequences in OEIS
> have missing representations as elliptic integrals, for example:
>
> https://oeis.org/A000172
>
> Perhaps it's obvious to some of us, but not to me, so I had to read
> the Weierstrass data from Stephan Herfurtner's thesis:
>
> g2 = 3/64 (1 + 12 x + 30 x^2 - 228 x^3 + 9 x^4)
> g3 = 1/512 (1 + 18 x + 99 x^2 + 684 x^3 + 3159 x^4 - 1566 x^5 - 27 x^6)
> (try searching OEIS for "herfurtner" to find the reference)
>
> Unfortunately I can't read French and German very well, so haven't
> tracked back Schmickler-Hirzebruch paper:
>
>
> https://mathoverflow.net/questions/220290/looking-for-schmickler-hirzebruch-monograph-on-elliptic-surfaces
>
> Many of the related OEIS sequences also refer cryptically to Beauville:
>
> >This is the Taylor expansion of a special point on a curve described by
> Beauville.
>
> Does anyone know if this means "period integral" or something else? I also
> have
> not been able to track back the Matthijs Coster reference (and don't even
> know
> where to start):
>
> > Matthijs Coster, Over 6 families van krommen [On 6 families of curves],
> > Master's Thesis (unpublished), Aug 26 1983.
>
> From an editorial point of view, ambiguity and missing references are
> problematic.
> But more in general I'm curious about publication history before and after
> the
> Herfurtner thesis.
>
> The Herfurtner thesis contains some beautiful results, which I think
> Picard, Goursat, Klein
> etc. would have paid attention to, had those results been known in
> previous lifetimes.
> How is it that Stephan Herfurtner's thesis has met with so little
> recognition and fanfare?
>
> One possibility is that contextual information is buried in French or
> German language
> articles not immediately accessible to an English language audience.
> Another possibility
> is that contextual information is part of an academic secret-keeping
> culture, which I
> think many of us would stand against. A third and most exciting
> possibility is that we
> simply have been slow to understand these rarefied tables, and are only
> now over the
> last few years finding contextual information to increase their relevance
> and value.
>
> Anyone with relevant information is welcome to write me. I'm especially
> petitioning
> native French and German speakers who have better skills than I do for
> this sort
> of research.
>
> In the meantime I will update some more of our references with data that I
> have
> from Herfurtner thesis, and probably add a few missing sequences as well.
>
> Thanks again,
>
> --Brad
>
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