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A level N reduction theory of indefinite binary quadratic forms

Carlos Castano-Bernard
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Abstract

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that this algorithm produces are such that the the corresponding paths γ_1, . . ., γ_n in the Riemann surface X0(N)(C) have a nice behavior around the elliptic points of order 2.

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Carlos Castano-Bernard. 2006-03-06. A level N reduction theory of indefinite binary quadratic forms. https://arxiv.org/abs/math/0603149

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