Related papers: Level Aspect Subconvexity For Rankin-Selberg $L$-f…

We consider the Rankin-Selberg L-functions associated with a fixed modular form of full level and holomorphic cuspidal newforms of large even weight, fixed level and fixed primitive nebentypus. We compute the second moment of this family in…

In this paper, we improve our bounds on the Rankin--Selberg problem. That is, we obtain smaller error term of the second moment of Fourier coefficients of a $\rm GL(2)$ cusp form (both holomorphic and Maass).

Sparse level-set formulations allow practitioners to find the minimum 1-norm solution subject to likelihood constraints. Prior art requires this constraint to be convex. In this letter, we develop an efficient approach for nonconvex…

In this paper, we develop a conditional subconvexity bound for Godement-Jacquet $L$-functions associated with Maass forms for $SL(3,Z)$.

Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^k$ with $p$ prime. In this paper we will prove the following subconvexity bound $$…

We compute an asymptotic formula for a moment involving the spinor and the standard $L$-functions for holomorphic Siegel cusp forms of degree two and large weight $k$. Applications include simultaneous non-vanishing statements and lower…

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex…

In this paper, we prove that a primitive Hilbert cusp form $\mathbf{g}$ is uniquely determined by the central values of the Rankin-Selberg $L$-functions $L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})$, where $\mathbf{f}$ runs through all…

We obtain a first moment formula for Rankin-Selberg convolution $L$-series of holomorphic modular forms or Maass forms of arbitrary level on $GL(2)$, with an orthonormal basis of Maass forms. One consequence is the best result to date,…

We use the uniqueness of various invariant functionals on irreducible unitary representations of PGL(2,R) in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new…

Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for $GL_3(\mathbb R)$, we obtain the first moment of central values of $L(s,f\otimes \phi)$, where…

We prove a subconvexity bound in the conductor aspect for $L(s,f,\chi)$ where $f$ is a half integer weight modular form. This $L$-function has analytic continuation and functional equation, but no Euler product. Due to the lack of an Euler…

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\GL_{1}$ and $\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present…

Let $P,M$ be a two primes such that $(P,M)=1$. Let $\Pi$ be a normalized Hecke-Maa\ss\ form on ${\rm{GL}}(4)$ of level $P$, and $\chi$ a primitive Dirichlet character modulo $M$. In this paper, we study the hybrid subconvexity problem for…

For convex co-compact subgroups of SL2(Z) we consider the "congruence subgroups" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions related to irreducible representations of the Galois group…

Let $\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ with unitary central character over a number field $F$. We prove the first unconditional zero density estimate for the set…

In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend the method of Michel-Venkatesh to reduce the bounds…

Blomer and Maga recently proved that, if $F$ is an $L^2$-normalized Hecke Maass cusp form for $\mathrm{SL}_n(\mathbb Z)$, and $\Omega$ is a compact subset of $\mathrm{PGL}_n(\mathbb R)/\mathrm{PO}_n(\mathbb R)$, then we have…

We study the low lying zeros of $GL(2) \times GL(2)$ Rankin-Selberg $L$-functions. Assuming the generalized Riemann hypothesis, we compute the $1$-level density of the low-lying zeroes of $L(s, f \otimes g)$ averaged over families of…

In this paper, we will give the subconvexity bounds for self dual GL(3) $L-$functions in the $t$ aspect as well as subconvexity bounds for self dual $GL(3)\times GL(2)$ $L-$functions in the GL(2) spectral aspect.