On the Rankin–Selberg problem, II

Abstract

In this paper, we improve our bounds on the Rankin–Selberg problem. That is, we obtain a smaller error term of the second moment of Fourier coefficients of a GL(2) cusp form (both holomorphic and Maass).

On the Fourier Coefficients for General Product 𝐿-Functions

“…The exponent in result (1.5) has recently been improved by Huang [10] to 3 5 − 𝛿 1 + 𝑜(1) with 𝛿 1 ≤ 1 560 . More recently, motivated by the Kowalski, Lin and Michel [26] concerning the Rankin-Selberg coefficients in large arithmetic progressions, Huang [14] further sharpen the exponent of the result to 3 5 − 𝛿 2 with 𝛿 2 = 3 305 . For 𝑙 = 3, the error term 𝐸 3 (𝑥) related to Fourier coefficients of triple product…”