Top, An

elliptic surface related to sums of consecutive squares, Exposition.

The vertex of the

elliptic surface is considered as the origin of the space coordinates.

1]), we obtain the Weierstrass model of the Jacobian elliptic surface [J.

Proposition Let Y be an elliptic surface over R given by the equation:

Finally, in section 7, we study topology of the real part R(R) for a real tetragonal curve embedded in an Hirzubruch surface and we show how one can use real elliptic surface with double real or complex conjugate section to compute topology of the real part for real tetragonal curves.

Proposition A real elliptic surface with double section (over C) is a (M - d)-variety if and only if is the associated tetragonal curve is a (M - d)--curve.

It is the group of sections of the elliptic surface [S.

lambda]], and the results obtained below for the elliptic surface can be directly translated to the results for the cubic surface.

Thus the elliptic surface [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (and the cubic surface [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) is defined by the Weierstrass equation:

Eleven contributions are selected from the eight working groups in the areas of

elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.

The aim of the experimental investigations was to correlate the predicted and real deviations of the curvature representation of

elliptic surfaces.

Ankara, Turkey) explores ramifications of the close relation between

elliptic surfaces and trigonal curves in ruled surfaces, skeletons (also called dessins d'enfants and quilts among other things), and subgroups of the modular group gamma : = PSL(2,Z).