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UID:news562@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190116T155209
DTSTART;TZID=Europe/Zurich:20131219T161500
SUMMARY:Perlen-Kolloquium: David Masser (Universität Basel)
DESCRIPTION:Functions  such  as 1/(x(x−λ))½ can  always  be  integrated
   (with  respect  to x)  in“elementary terms” involving logarithms and
  exponentials. But not 1/(x(x−1)(x−λ))½ unless λ=0\,1. A more inter
 esting example is 1/((x−1+λ3)(x(x−1)(x−λ))½)\, which can be done 
 also for λ=(1+(−3)½)/2. In 1981 James Davenport claimed that an arbitr
 ary such algebraic f(x\,λ) can be integrated for at most finitely many sp
 ecial complex values λ (unless it can be integrated for a general value o
 f λ). Umberto Zannier and Idare to hope for a full proof in the next coup
 le of years\; but for now I will content myself with a general discussion 
 of the problem together with some of the key concepts involved in settling
  significant special cases.
X-ALT-DESC: Functions  such  as 1/(x(x−λ))<sup>½ </sup>can  always  be 
  integrated  (with  respect  to x)  in“elementary terms” involving log
 arithms and exponentials. But not 1/(x(x−1)(x−λ))<sup>½</sup> unless
  λ=0\,1. A more interesting example is 1/((x−1+λ3)(x(x−1)(x−λ))<s
 up>½</sup>)\, which can be done also for λ=(1+(−3)<sup>½</sup>)/2. In
  1981 James Davenport claimed that an arbitrary such algebraic f(x\,λ) ca
 n be integrated for at most finitely many special complex values λ (unles
 s it can be integrated for a general value of λ). Umberto Zannier and Ida
 re to hope for a full proof in the next couple of years\; but for now I wi
 ll content myself with a general discussion of the problem together with s
 ome of the key concepts involved in settling significant special cases.
DTEND;TZID=Europe/Zurich:20131219T190000
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