Mixed integral moments of the Hecke $L$-functions and Riemann zeta function

In this paper, let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We establish an asymptotic formula for the mixed moment of $ζ^{2}(s)$ and $L(s,f)$ on the critical line, valid for both holomorphic and Maass forms.

💡 Research Summary

The paper studies a mixed moment involving a Hecke L‑function attached to a cusp form $f$ on the full modular group $SL(2,\mathbb Z)$ and the Riemann zeta‑function on the critical line. While most previous work on moments of $L$‑functions deals either with absolute values (e.g. $\int_0^T|L(\tfrac12+it,f)\zeta(\tfrac12+it)|^2dt$) or with moments of a single $L$‑function, this article establishes an asymptotic formula for the non‑absolute mixed moment \