Jan-Christoph Schlage-Puchta
A problem of Ramanujan, Erdos and Katai on the iterated divisor function.
Ср, 08/10/2011 - 15:01 — SomNambulAuthors: Jan-Christoph Schlage-Puchta, Kevin Ford, Yvonne Buttkewitz, Christian Elsholtz
Subjects: Number Theory
AbstractWe determine asymptotically the maximal order of log d(d(n)), where d(n) is
the number of positive divisors of n. This solves a problem first put forth by
Ramanujan in 1915.- 1 комментарий
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An inequality for means with applications.
Втр, 05/10/2011 - 15:01 — SomNambulAuthors: Jan-Christoph Schlage-Puchta
Subjects: Probability
AbstractWe show that an almost trivial inequality for the first and second mean of a
random variable can be used to give non-trivial improvements on deep results.
As applications we improve on results on lower bounds for the Riemann
zeta-function on the critical line, the determinant of a skew-symmetric matrix
with entries $\pm 1$, and on the maximal order of an irreducible character of
the symmetric group.Meromorphic Continuation of the Goldbach generating function.
Пт, 02/26/2010 - 16:01 — SomNambulAuthors: Gautami Bhowmik, Jan-Christoph Schlage-Puchta
Subjects: Number Theory
AbstractWe consider the Dirichlet series associated to the number of representations
of an integer as the sum of primes. Assuming the Riemann hypothesis on the
distribution of the zeros of the Riemann zeta function we obtain the domain of
meromorphic continuation of this series.Essential singularities of Euler products.
Ср, 01/13/2010 - 16:01 — SomNambulAuthors: Gautami Bhowmik, Jan-Christoph Schlage-Puchta
Subjects: Number Theory
AbstractWe classify singularities of Dirichlet series having Euler products which are
rational functions for p and p^{-s} for p a prime number and give examples of
natural boundaries from zeta functions of groups and height zeta functions.
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