A level N reduction theory of indefinite binary quadratic forms

2006/03/06 by Carlos Castaño-Bernard, Castano-Bernard, Carlos · 1 citation
Computer Science · Mathematics · #11E16 #20H05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0603149

openalex publication_date 2006/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ⁰(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q₁, . . ., Q_n that this algorithm produces are such that the the corresponding paths γ₁, . . ., γ_n in the Riemann surface X0(N)(C) have a nice behavior around the elliptic points of order 2.

Cited by

• The Triangular Theorem of the Primes: Binary Quadratic Forms and Primitive Pythagorean Triples

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