# The G.-C. Rota approach and the Lehmer conjecture

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Speaker:
Bernhard Heim
Zugehörigkeit:
German University of Technology, Oman (GUtech) and RWTH Aachen
Datum:
Die, 2019-08-06 14:30 - 15:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar

Report on joint work with M. Neuhauser. This includes results with C. Kaiser, F. Luca, F. Rupp,
R. Troeger, and A. Weisse.
The Lehmer conjecture and Serre's lacunary theorem describe the vanishing properties of the Fourier
coefficients of even powers of the Dedekind eta function.
G.-C. Rota proposed to translate and study problems in number theory and combinatorics to and via
reciprocals of the cubic root of Klein's absolute $j$-invariant, and hence the $j$-invariant itself.
Finally we give an interpretation of the first non-sign change of the Ramanujan $\tau(n)$ function by