Sums of coefficients of general L-functions over arithmetic progressions and applications

In this paper, we study the asymptotic distribution of coefficients of general L-functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for Gamma = SL(2, Z) over arithmetic progressions, and improve the results of Jiang and L & uuml; [10]. Our new results remove the restriction to prime module and improve the interval length of module q. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.