THE JACOBIAN OF A QUOTIENT HIPERELÍPTICO THE CURVE FERMAT AND THE LAW OF RECIPROCITY FOR THE POWERS SEVENTHSAuthor:
ECHARRI HERNÁNDEZ JOSE MIGUEL.
Year:
2005.
University:
PAÍS VASCO [
www.ehu.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.
Summary: The aim of this thesis is to give a demonstration of the law of reciprocity for the symbol of the powers sevenths, using the arithmetic of the curve Y2 = X7 + 1 / 4, which is a curve hiperelíptica gender three. His main inspiration has been an article of D. Grant in which test the law of reciprocity for the symbol of the powers fifths from the arithmetic of the curve Y2 = X5 + 1 / 4, which is a curve hiperelíptica gender two. Replying to a question raised explicitly in this article we show how it follows the law of reciprocity for the symbol of the powers sevenths from the arithmetic of a curve that is rational image of the curve Fermat for p = 7. The main techniques used are the study group's formal origin of the Jacobian and theorems of complex multiplication. Moreover, to test the laws built-up units similar to those units classic elliptical rational functions in assessing points of torque.
