Prof. Dr. Jens Franke


Freitags, von 14.20 bis 15.20, in meinem Büro (1.026).

Vorlesung "Algebra I"

The discussion of the results of the first exam is on Wednesday August 16 in room 0.011.

A few remarks about the principles I followed in assigning points and grades to the solutions. As I stated clearly, I was interested in the complete formulations of results from other parts the lecture used in the proof, in order to be able to check wheter you understand the precise assumptions under which the result you are using holds. Unfortunately, this was often disregarded. To limit the consequences of this for your grade, I interpreted "formulating the assumptions" liberally. Also, I decided not to punish the first shortcoming of this type and to limit the total number of points subtracted in such cases to two.

Not checking that the poset to which Zorn's lemma is applied in the solution to Problem 2 is non-empty was also included in the set of minor mistakes for which I decided not to punish the first occurance. On participant, unfortunately, checked the "bound on totally ordered chains"-part of the assumptions of Zorn's lemma only for countable chains. I would like to point out for all participants that this form of Zorn's lemma is wrong, the set of countable subsets of some uncountable set (like R), partially ordered by inclusion, being an obvious counterexample.

Seminar "Geometrische Konstruktionen und transzendente Zahlen."

Das Seminar fand im Sommersemester 2016 für Studenten des zweiten Semesters statt. Um einen guten Anschluß an die Vorlesung "Lineare Algebra I" sicherzustellen, diente ein von mir selbst verfaßter Text als Grundlage des Seminares. Dieser soll hier weiterhin zur Verfüfung gestellt werden.

Vorlesungen "Mathematik für Physiker I-III"

Die Javascript-Programme zu den Anwesenheitsübungen dieser Vorlesungen, die ich zwischen 2008 und 2011 gehalten habe, sind weiterhin online:

Selected Publications

  • On the spaces Fspq of Triebel-Lizorkin type: pointwise multipliers and spaces on domains, Math. Nachr. 125 (1986), 113-149.
  • (with Yu. I. Manin and Yu. Tschinkel) Rational points of bounded height on Fano varieties, Invent. Math. 95(1989), 421-435
  • (with T. Runst) Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces. Math. Nachr. 174 (1995), 113-149.
  • Harmonic analysis in weighted L2-spaces, Ann. Sci. École Norm. Sup. (4), 31(1998), 181-279
  • (with J. Schwermer), A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups, Math. Ann. 311(1998), 765-790.
  • On the singularities of residual Eisenstein series, Invent. Math. 138(1999), 307-317
  • (With T. Kleinjung, F. Morain and T. Wirth) Proving the primality of very large numbers with fastECPP, in Algorithmic number theory, Lecture Notes in Comput. Sci., 3076, 2004, pages 194-207.
  • (With T. Kleinjung), Continued fractions and lattice sieving. In: Proceedings SHARCS 2005
  • (with K. Aoki, T. Kleinjung, A. Lenstra, D. Osvik) A kilobit special number field sieve factorization, in Advances in cryptology. ASIACRYPT 2007, Lecture Notes in Comput. Sci., 4833, 2007, pages 1-12.
  • A topological model for some summand of the Eisenstein cohomology of congruence subgroups, in Eisenstein series and applications, Progr. Math., 258, 2008, pages 27-85.