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On an incomplete argument of Erdos on the irrationality of Lambert series
Lambert series divisor function q-logarithm Number Theory
2012/6/15
We show that the Lambert series $f(x)=\sum d(n) x^n$ is irrational at $x=1/b$ for negative integers $b < -1$ using an elementary proof that finishes an incomplete proof of Erdos.
On computing the generalized Lambert series
computing generalized Lambert series Theta convergence ODEs
2012/3/1
We show how the generalized Lambert series sum(n>=1, x*q^n/(1-x*q^n)) can be computed with Theta convergence. This allows the computation of the sum of the inverse Fibonacci numbers without splitting ...