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4 papers
Computing Galois representations and equations for modular curves
Maarten Derickx, Mark van Hoeij, Jinxiang Zeng
We construct plane models of the modular curve , and use their explicit equations to compute Galois representations associated to modular forms for values of that…
Computing points on modular curves over finite fields
Jinxiang Zeng
In this paper, we present a probabilistic algorithm to compute the number of -points of modular curve . Under the Generalized Riemann Hypothesis(GRH), the alg…
On the computation of coefficients of modular forms: the reduction modulo p approach
Jinxiang Zeng, Linsheng Yin
In this paper we present a probabilistic algorithm to compute the coefficients of modular forms of level one. Focus on the Ramanujan's tau function, we give out the explicit comple…
Factoring integer using elliptic curves over rational number field
Xiumei Li, Jinxiang Zeng
For the integer of the product of two distinct odd primes, we construct an elliptic curve over , where is a parameter dependent on the…