Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1.913-25, to the Lichtquanten hypothesis of Einstein. Some episodes with H.A. Kramers, J.C. Slater and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavour to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.Comment: 15 page

Relation of the cyclotomic equation with the harmonic and derived series

We associate some (old) convergent series related to definite integrals with the cyclotomic equation $x^m-1= 0$, for several natural numbers $m$; for example, for $m = 3$, $x^3-1 = (x-1)(1+x+x^2)$, leads to $\int_0^1dx\frac{1}{(1+x+x^2)} = \frac{\pi}{(3\sqrt{3})} = (1-\frac{1}{2}) + (\frac{1}{4}-\frac{1}{5}) + (\frac{1}{7}-\frac{1}{8}) + \ldots$ . In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary $m$ are well defined, but do imply integrals and/or series summations rather involved.Comment: This paper has been accepted in The Scientific World Journal, and will appear in brie