 CARMA SEMINAR
 Speaker: Florian Luca, Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México
 Title: Linear independence of certain Lambert series
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Wed, 13^{th} Mar 2013
 Abstract:
We prove that if $q\ne0,\pm1$ and $\ell\ge1$ are fixed
integers, then the numbers
$$
1, \quad \sum_{n=1}^\infty\frac{1}{q^n1},
\quad \sum_{n=1}^\infty\frac{1}{q^{n^2}1}, \quad \dots,
\quad \sum_{n=1}^\infty\frac{1}{q^{n^\ell}1}
$$
are linearly independent over $\mathbb{Q}$. This generalizes a result
of Erdős who treated the case $\ell=1$.
The method is based on the original approaches of Chowla and
Erdős, together with some results about primes in arithmetic
progressions with large moduli of Ahlford, Granville and Pomerance.
This is joint work with Yohei Tachiya.
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