75 citations · 114 across the 41 of their papers we have counts for
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The transcendence of via formal power series
Martin Klazar
We review Hilbert's classical analytical proof of the transcendence of the number . Then, we show how this result can be obtained algebraically by means of formal power…
Birch's theorem: if f(n) is multiplicative and has a non-decreasing normal order then f(n)=n^{alpha}
Martin Klazar
For pedagogical purposes (inclusion in lecture notes) we review the proof of the theorem stated in the title. At the end we state a problem.
Counting Keith numbers
Martin Klazar, Florian Luca
A Keith number is a positive integer N with the decimal representation a_1a_2...a_n such that n>=2 and N appears in the sequence (K_m) given by the recurrence K_1=a_1,...,K_n=a_n a…
On the maximal order of numbers in the "factorisatio numerorum" problem
Martin Klazar, Florian Luca
Let m(n) be the number of ordered factorizations of n in factors larger than 1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog n)^{1+eps}] holds for all i…