Related papers: $t$-aspect subconvexity for $GL(2) \times GL(2)$ $…

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…

Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $\chi$ be a primitive character of prime-power modulus $q = p^{\gamma}$. In this paper, we prove the following hybrid Weyl-type subconvexity bound…

Let $\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that…

Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $\chi$ be a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa>12$. A subconvex bound for the…

We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where the second moment is a sum over $t_j$ in a short interval. At the central point…

We compute an asymptotic formula for the twisted moment of GL(3)xGL(2) L-functions and their derivatives. As an application we prove that symmetric-square lifts of GL(2) Maass forms are uniquely determined by the central values of the…

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…

Let $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…

Let $f$ and $g$ be normalized Hecke-Maass cusp forms for the full modular group having spectral parameters $t_f$ and $t_g$ respectively with $t_f,t_g\asymp T\rightarrow \infty $. In this paper we show that the Rankin Selberg $L$-function…

In this paper, we introduce a simple Bessel $\delta$-method to the theory of exponential sums for $\rm GL_2$. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level…

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

In this paper we generalized Venkatesh and Woodbury's work on the subconvexity bound of triple product L-function in level aspect, allowing joint ramifications, higher ramifications, general unitary central characters and general special…

We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical conductor of $\chi$, where $\pi$ is a $GL_2$ cuspidal representation and $\chi$ is a Hecke character.

This is a sequel to our previous articles \cite{Kw23, Kw23a+}. In this work, we apply recent techniques that fall under the banner of `Period Reciprocity' to study moments of $GL(3)\times GL(2)$ $L$-functions in the non-archimedean aspects,…

Let $\pi$ be a fixed Hecke--Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be a prime. Let $L(s,\pi\otimes \chi)$ be the $L$-function associated to $\pi\otimes…

We compute the second moment of a certain family of Rankin-Selberg $L$-functions L(f x g, 1/2) where f and g are Hecke-Maass cusp forms on GL(n). Our bound is as strong as the Lindel\"of hypothesis on average, and recovers individually the…

We establish a sub-convexity estimate for Rankin-Selberg $L$-functions in the combined level aspect, using the circle method. If $p$ and $q$ are distinct prime numbers, $f$ and $g$ are non-exceptional newforms (modular or Maass) for the…

In this paper we prove a new subconvexity result for the standard L-function of a unitary cuspidal automorphic representation $\pi$ of $\text{GL}_n$, where the finite set of places $S$ with large conductors is allowed to vary, provided that…

Let $F$ be a self-dual Hecke-Maa\ss\ form for ${\rm{GL}}(3)$ underlying the symmetric square lift of a ${\rm{GL}}(2)$-newform of square-free level and trivial nebentypus. In this paper, we are interested in the first moments of the central…

In this paper, we obtain a subconvexity result for the Rankin-Selberg L-function in both levels. The new feature in this result is applying an amplification method of Duke-Friedlander-Iwaniec to a double Petersson-Kuznetsov trace formula.…