2025/07/22 by Tianyu Ni, Hui Xue, Ni, Tianyu +1
Mathematics · #11F11 #11F67 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2507.17041
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Sk denote the space of cusp forms of weight k and level one. For 0≤ t≤ k-2 and primitive Dirichlet character χ mod D, we introduce twisted periods rt,χ on Sk. We show that for a fixed natural number n, if k is sufficiently large relative to n and D, then any n periods with the same twist but different indices are linearly independent. We also prove that if k is sufficiently large relative to D then any n periods with the same index but different twists mod D are linearly independent. These results are achieved by studying the trace of the products and Rankin-Cohen brackets of Eisenstein series of level D with nebentypus. Moreover, we give two applications of our method. First, we prove certain identities that evaluate convolution sums of twisted divisor functions. Second, we show that Maeda's conjecture implies a non-vanishing result on twisted central L-values of normalized Hecke eigenforms.