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Ramanujan sums for signal processing of low-frequency noise.
This work introduces a different signal processing tool based on the Ramanujan sums c(q)(n), well adapted to the analysis of arithmetical sequences with many resonances p/q, and different results arise from the use of thisRamanujan-Fourier transform in the context of arathmetical and experimental signals. Expand
A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shownExpand
Close to resonance interaction of radiofrequency waves in a Schottky diode mixer: 1/f noise and number theory
1/f noise arising from the mixing and phase locking of two input radio frequency oscillators in a doubly balanced phase bridge with Schottky diodes is investigated. It is interpreted from numberExpand
A new aspect of Some Post algebras
Some Post algebras are nothing but commutative unitary algebras L over a finite field K where Fermat theorem holds in L.
About some diophantine equation and the resulting chaos in geodesics
We announce results about a complete Markoff theory for the diophantine equation: x2+y2+z2=3xyz+2x All its solutions can be computed. For positive integers, they are organized in two trees. WithExpand
Ramanujan sums, low frequency noise and quantum phase-locking
An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Mobius function or Mangoldt function, which are coding sequences forExpand
Approximation diophantienne (théorie de Markoff)
Towards 1880, A. Markoff gave precisions about structure of the set of approximation constants greater than 1/3 for irrational numbers. This theory establishes links between constants, arithmeticalExpand
Mathematics and music. a diderot mathematical forum
In a former work, recalling what the Markoff theory is, we summarized some existing links with the group GL(2, ℤ) of 2 × 2 matrices. We also quoted the relation with conformal punctured toruses. TheExpand