arXiv subjects

Suraj Panigrahy

Publications and source records attributed to Suraj Panigrahy.

2 recordsLinked to original sources

arXiv2026

Short Second Moment of $\mathrm{GL}(2)$ L-Functions via Trivial Delta

Let $f$ be a holomorphic cusp form for $SL(2,\mathbb{Z})$. In this paper, we prove for $T^{\frac{1}{3}} \ll M \ll T^{\frac{1}{2}}$, the following short interval second moment \begin{equation*} \int_T^{T+M}\left|L\left(\frac12+it,f\right) \right|^2 dt \ll_{f,\epsilon} T^\epsilon \left( M + \frac{T}{M}+\sqrt{TM}\right). \end{equation*} The proof uses the trivial delta method along with conductor lowering technique.

math.NT↗

arXiv2026

Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions

For $M_1$ and $ M_2$ two distinct primes, let $ H_k^\star(M_1M_2, ψ)$ denote the set of primitive newforms of level $M_1M_2$, weight $k\geq 3$ and Nebentypus $ψ$ of conductor $M_1$. Let $π$ be a fixed $SL(3, \mathbb{Z})$ Hecke cusp form. We prove a Lindelöf--consistent upper bound for the second moment \[ \mathop{ \sum_{\substack{ψ(M_1) \\ ψ(-1)=(-1)^k }}} \sideset{}{^h}\sum_{f \in H_k^{\star}(M_1M_2,ψ)} |L(1/2, π\times f)|^2 \ll_{π,ε} M_1^{1+ε}\] in the range $M_2\leq M_1^{1+ε}$.

math.NT↗