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Symmetry and folding of continued fractions

Alfred J. Van der Poorten (2002)

Journal de théorie des nombres de Bordeaux

Michel Mendès France's “Folding Lemma” for continued fraction expansions provides an unusual explanation for the well known symmetry in the expansion of a quadratic irrational integer.

Symmetry of iteration graphs

Walter Carlip, Martina Mincheva (2008)

Czechoslovak Mathematical Journal

We examine iteration graphs of the squaring function on the rings / n when n = 2 k p , for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when k = 3 and when k 5 and are symmetric when k = 4 .

Symplectic periods.

Hervé Jacquet, Stephen Rallis (1992)

Journal für die reine und angewandte Mathematik

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

Rolf-Peter, Holzapfel (1997)

Serdica Mathematical Journal

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system....

Systèmes d’Euler p -adiques et théorie d’Iwasawa

Bernadette Perrin-Riou (1998)

Annales de l'institut Fourier

On définit la notion de système d’Euler associé à une représentation p -adique V du groupe de Galois absolu de dans le cas cyclotomique. Cette notion a été introduite par Kolyvagin. L’existence d’un tel système a des conséquences très importantes sur l’étude des groupes de Selmer de V que nous développons ici.

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