2025/12/05 by Gao, Peng, Wu, Xiaosheng
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2512.05378
For any large prime q, 1 ≤ x ≤ q and any real 0 ≤ k ≤ 1, we prove an upper bound for the following 2k-th moment ∑_\substackχ\bmod q | ∑n≤ x χ(n)λ(n)|2k, where λ(n) denotes the Fourier coefficients of a fixed modular form. In particular, our result implies that \frac 1q-1∑_\substackχ\bmod q | ∑n≤ x χ(n)λ(n)|= o(√(x)), when both x and q/x tend to infinity with q.