Sign changes in Fourier coefficients of the symmetric power L-functions on sums of two squares

2025/02/21 by Kaur, Amrinder
#11F11 #11F30 #11F41 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.15207

Abstract

Let f be a normalized primitive Hecke eigen cusp form of even integral weight k for the full modular group SL(2,ℤ). For integers j ≥ 2, let λ_{sym^j f}(m) denote the mth Fourier coefficient of the jth symmetric power L-function associated with f. We give a quantitative result on the number of sign changes of λ_{sym^j f}(m) for the indices m that are the sum of two squares in the interval [1,x] for sufficiently large x.

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