模形式傅里叶系数中多项式的除数矩
Divisor moments of polynomials in Fourier coefficients of modular forms
AI总结：
研究非CM新形式傅里叶系数多项式表达式上除数函数高阶矩，证明中对数指数取决于多项式不可约因子数且在佐藤-泰特限制下不变，结合多种定理及算术、均值估计得出结论。
AI中文摘要：
我们研究了在非CM新形式的傅里叶系数的多项式表达式上求值的除数函数的高阶矩。我们估计中出现的对数指数仅取决于多项式的不可约因子的数量，并且在佐藤-泰特限制下保持不变。证明结合了有效的切博塔廖夫定理或有效的切博塔廖夫-佐藤-泰特定理，联合循环类型的算术以及具有弗罗贝尼乌斯支撑的多变量乘法函数的均值估计。
英文摘要：
We study higher moments of the divisor function evaluated at polynomial expressions in the Fourier coefficients of a non-CM newform. The logarithmic exponent appearing in our estimates depends only on the number of irreducible factors of the polynomial and remains unchanged under a Sato--Tate restriction. The proof combines an effective Chebotarev theorem, or an effective Chebotarev--Sato--Tate theorem, with the arithmetic of joint cycle types and a mean value estimation for multivariable multiplicative functions with Frobenian support.
