论文标题
椭圆形$ j $ invariant的模块化多项式系数的明确界限
Explicit bounds on the coefficients of modular polynomials for the elliptic $j$-invariant
论文作者
论文摘要
对于任何$ n \ geq1 $，我们获得了椭圆模块多项式$φ_n$的系数大小的显式上限。这些多项式在$ j $ invariants的椭圆曲线上消失，由$ n $的循环同学连接。边界中的主要术语在$ n $上是渐近的最佳选择。
We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials $Φ_N$ for any $N\geq1$. These polynomials vanish at pairs of $j$-invariants of elliptic curves linked by cyclic isogenies of degree $N$. The main term in the bound is asymptotically optimal as $N$ tends to infinity.
