ﻻ يوجد ملخص باللغة العربية
Let $ mathfrak{f} $ run over the space $ H_{4k} $ of primitive cusp forms of level one and weight $ 4k $, $ k in N $. We prove an explicit formula for the mixed moment of the Hecke $ L $-function $ L(mathfrak{f}, 1/2) $ and the symmetric square $L$-function $ L(sym^2mathfrak{f}, 1/2)$, relating it to the dual mixed moment of the double Dirichlet series and the Riemann zeta function weighted by the ${}_3F_{2}$ hypergeometric function. Analysing the corresponding special functions by the means of the Liouville-Green approximation followed by the saddle point method, we prove that the initial mixed moment is bounded by $log^3k$.
We study simultaneous non-vanishing of $L(tfrac{1}{2},di)$ and $L(tfrac{1}{2},gotimes di)$, when $di$ runs over an orthogonal basis of the space of Hecke-Maass cusp forms for $SL(3,mathbb{Z})$ and $g$ is a fixed $SL(2,mathbb{Z})$ Hecke cusp form of weight $kequiv 0 pmod 4$.
Let $phi$ be a Hecke-Maass cusp form for $SL(3, mathbb{Z})$ with Langlands parameters $({bf t}_{i})_{i=1}^{3}$ satisfying $$|{bf t}_{3} - {bf t}_{2}| leq T^{1-xi -epsilon}, quad , {bf t}_{i} approx T, quad , , i=1,2,3$$ with $1/2 < xi <1$ and any $ep
In this article, we will prove subconvex bounds for $GL(3) times GL(2)$ $L$-functions in depth aspect.
Let $F$ be a $G L(3)$ Hecke-Maass cuspform of level $P_1$ and $f$ be a $G L(2)$ Hecke-Maass cuspform of level $P_2$. In this article, we will prove a subconvex bound for the $G L(3) times G L(2)$ Rankin-Selberg $L$-function $L(s,Ftimes f)$ in the lev
In this paper we shall prove a subconvexity bound for $GL(2) times GL(2)$ $L$-function in $t$-aspect by using a $GL(1)$ circle method.