On modular equations
نویسندگان
چکیده
منابع مشابه
On Certain Modular Equations
We present the MEoP problem that decides the existence of solutions to certain modular equations over prime numbers and show how this separates the complexity class NP from its subclass P.
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Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup Γ0(N), as an algebraic transformation of elliptic curve periods, parametrized by a Hauptmodul (function field generator). The periods satisfy a Picard–Fuchs equation, of hypergeometric, Heun, or more general type; so the new modular equati...
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We define modular equations describing the `-torsion subgroups of the Jacobian of a hyperelliptic curve. Over a finite base field, we prove factorization properties that extend the well-known results used in Atkin’s improvement of Schoof’s genus 1 point counting algorithm.
متن کاملModular equations and eta evaluations
My talk at the recent AustMS annual meeting met with some success [1], immediately initiating a request that I write a summary for the Gazette. In response, I give an informal essay surveying the ideas which precipitated my interest in modular equations.
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Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1897
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1897-00414-1