9. přednáška 24. 4. 2015. Dirichlet's theorem on prime numbers in arithmetic progression.
We are almost finished
, it just remains to prove Propositions 1, 2, and 3 on group characters. (by
these preliminary lecture notes.)
1. 5. and 8. 5. no lecture - state holidays
10. přednáška 15. 5. 2015. Prof of propositions 1, 2, and 3 on group characters.
11. přednáška 22. 5. 2015. 5. Some basic properties of Riemann's zeta function. According to the beginning of Titchmarh's tract on zeta function. See
here
(scan of the relevant pages, more material than I covered in the lecture). A combinatorial
application: if f(n) = the number of ordered factorizations of n
into numbers > 1then limsup (f(n) / log n) = alpha, where
zeta(alpha) = 2 (in the lecture I mentioned only the lower bound >
alpha - ep; the upper bound follows from Landau's theorem (abscissa of
convergence of a Dirichlet series with nonnegative coefficients is a
singularity of the function given by the series)).