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Ramanujan sums for signal processing of low-frequency noise.

- M. Planat, H. Rosu, Serge Perrine
- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and…
- 1 September 2002

TLDR

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

- M. Planat, H. Rosu, Serge Perrine
- Mathematics, Physics
- 14 September 2004

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 shown… Expand

Close to resonance interaction of radiofrequency waves in a Schottky diode mixer: 1/f noise and number theory

- M. Planat, S. D. Santos, N. Ratier, J. Cresson, Serge Perrine
- Mathematics
- 2 April 1999

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 number… Expand

A new aspect of Some Post algebras

- Serge Perrine
- Computer Science, Mathematics
- MVL '78
- 1978

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

- Serge Perrine
- Mathematics
- 14 August 2001

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. With… Expand

Ramanujan sums, low frequency noise and quantum phase-locking

- M. Planat, H. Rosu, Serge Perrine
- Mathematics
- 2002

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 for… Expand

Approximation diophantienne (théorie de Markoff)

- Serge Perrine
- Art
- 1988

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, arithmetical… Expand

Un arbre de constantes d'approximation analogue à celui de l'équation diophantienne de Markoff

- Serge Perrine
- Mathematics
- 1998

MONODROMY ARISING FROM THE MARKOFF THEORY

- Serge Perrine
- Mathematics
- 20 May 2006

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. The… Expand

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