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In einer 10-adischen Welt wird die Zahl 2016 so geschrieben 2016=6*1+1*10+0*100+2*1000. Was wäre es, wenn man mit p-adischen Zahlen zahlt? Zum Beispiel in einer 3-adischen Welt würde man eine ganze Zahl so geschrieben ?*1+?*3+?*9+?*27+… In diesem Seminar studieren wir p-adische Zahlen wenn p eine Primzahl ist.
Prerequistes: 1) very basic knowledge about algebra and topology, for example the notion of field, ring, topological space. 2) a certain familiarity with undergraduate level analysis, for example the notion continuous functions, convergent sequences, power series.
We count using 10-adic numbers. For example 2016=6*1+1*10+0*100+2*1000. What if we move into a p-adic world and count using p-adic numbers? For example in a 3-adic world we should write numbers as ?*1+?*3+?*9+?*27+… The main object of study in this course is the p-adic number counting systems when p is a prime number. If you have some other suggestions or questions, please contact me via l.zhang@fu-berlin.de. Hope to see you soon!