A Level N Reduction Theory of Indefinite Binary Quadratic Forms
نویسنده
چکیده
In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup Γ(N), with respect to the usual fundamental domain FN , where N is assumed prime. The cycles Q1, . . . , Qn that this algorithm produces are such that the the corresponding paths γ1, . . . , γn in the Riemann surface X0(N)(C) have a nice behaviour around the elliptic points of order 2.
منابع مشابه
Binary quadratic forms and Eichler orders
For any Eichler order O(D,N) of level N in an indefinite quaternion algebra of discriminant D there is a Fuchsian group Γ(D,N) ⊆ SL(2,R) and a Shimura curve X(D,N). We associate to O(D,N) a set H(O(D,N)) of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to Γ(D,N), for primitive forms contained in H(O(D,N)). In particul...
متن کاملOn Indefinite Binary Quadratic Forms and Quadratic Ideals
We consider some properties of indefinite binary quadratic forms F (x, y) = ax +bxy−y of discriminant ∆ = b +4a, and quadratic ideals I = [a, b−√∆ ]. AMS Mathematics Subject Classification (2000): 11E04, 11E12, 11E16
متن کاملThe family of indefinite binary quadratic forms and elliptic curves over finite fields
In this paper, we consider some properties of the family of indefinite binary quadratic forms and elliptic curves. In the first section, we give some preliminaries from binary quadratic forms and elliptic curves. In the second section, we define a special family of indefinite forms Fi and then we obtain some properties of these forms. In the third section, we consider the number of rational poi...
متن کاملDefinite Quadratic Forms over Fq[x]
Let R be a principal ideal domain with quotient field F . An R-lattice is a free R-module of finite rank spanning an inner product space over F . The classification problem asks for a reasonably effective set of criteria to determine when two given R-lattices are isometric; that is, when there is an inner-product preserving isomorphism carrying one lattice onto the other. In this paper R is the...
متن کاملAsymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms
Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of the class numbers by using the prime geodesic theorems for the congruence subgroups of the modular group.
متن کامل