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Eichler integrals play an integral part in the modular parametrizations of elliptic curves. In her master’s thesis, Kodgis conjectures several dozen zeros of Eichler integrals for elliptic curves with conductor ≤ 179. In this paper we prove a general theorem which confirms many of these conjectured zeros. We also provide two ways to generate infinite families of elliptic curves with certain zer...
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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...
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Let B be a quaternion algebra over number field K : Assume that B satisfies the Eichler condition (i.e., there is at least one archimedean place which is unramified in B). Let O be an order in a quadratic extension L of K: The Eichler orders of B which admit an embedding of O are determined. This is a generalization of Chinburg and Friedman’s embedding theorem for maximal orders. r 2004 Elsevie...
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ژورنال
عنوان ژورنال: Oesterreichische Botanische Zeitschrift
سال: 1887
ISSN: 0378-2697,1615-6110
DOI: 10.1007/bf01648870