Computing isogeny covariant differential modular forms
نویسندگان
چکیده
منابع مشابه
Computing isogeny covariant differential modular forms
We present the computation modulo p2 and explicit formulas for the unique isogeny covariant differential modular form of order one and weight χ−p−1,−p called fjet, an isogeny covariant differential modular form of order two and weight χ−p2−p,−1,−1 denoted by fjethjet, and an isogeny covariant differential modular form hjet of order two and weight χ1−p2,0,−1.
متن کاملExplicitly Computing Modular Forms
This is a textbook about algorithms for computing with modular forms. It is nontraditional in that the primary focus is not on underlying theory; instead, it answers the question “how do you explicitly compute spaces of modular forms?”
متن کاملModular Isogeny Complexes
We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations for Morava E-theory at height 2.
متن کاملModular forms and differential operators
A~tract, In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for each n i> 0 a bilinear operation which assigns to two modular forms f and g of weight k and l a modular form If, g], of weight k + l + 2n. In the present paper we study these "Rankin-Cohen brackets" from t w o points of view. On the one hand we give ...
متن کاملModular polynomials via isogeny volcanoes
We present a new algorithm to compute the classical modular polynomial Φl in the rings Z[X,Y ] and (Z/mZ)[X, Y ], for a prime l and any positive integer m. Our approach uses the graph of l-isogenies to efficiently compute Φl mod p for many primes p of a suitable form, and then applies the Chinese Remainder Theorem (CRT). Under the Generalized Riemann Hypothesis (GRH), we achieve an expected run...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2004
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-04-01721-1