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Amrinder Kaur

Publications and source records attributed to Amrinder Kaur.

5 recordsLinked to original sources
arXiv2025

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

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

math.NT↗
arXiv2023

On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II

In this paper, we consider the $k$-th Riesz mean for the coefficients of the Rankin-Selberg $L$-function $L_{f \times f}(s)$ related to the Godement-Jacquet $L$-function with respect to $SL(n,\mathbb{Z})$. We establish an asymptotic formula for the $k$-th Riesz mean with an improved range and a better error term. As a result, we get an asymptotic relation for the partial sum of the coefficients of $L_{f \times f}(s)$.

math.NT↗