Related papers: Subconvexity bounds for twisted L-functions, II

We prove an asymptotic for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line, conditionally on GRH. We derive the…

We prove an analogue of Heath-Brown's bound on the twelfth moment of the Riemann zeta function for Dirichlet L-functions with smooth moduli.

We give lower bounds of the conjectured order of magnitude for an orthogonal and a symplectic family of L-functions.

We evaluate the twisted first moment of central values of the product of a quadratic Dirichlet $L$-function and a quadratic twist of a modular $L$-function.

We obtain a strong bound on the second moment of the $GL_3$ standard $L$-function on the critical line. The method builds on the recent work of Aggarwal, Leung, and Munshi which treated shorter intervals. We deduce some corollaries…

We prove Lindel\"of-on-average upper bounds on the cubic moment of central values of $L$-functions over certain families of $\operatorname{PGL}_2/\mathbb{Q}$ automorphic representations $\pi$ given by specifying the local representation…

Extending a result of Heath-Brown, we establish an asymptotic formula for the fourth moment of central values of Dirichlet $L$-functions attached to primitive characters $\pmod q$.

We compute the first moment of twisted Hecke $L$-functions of prime power level going to infinity, uniformly in the conductor of the twist and in the vertical shift.

In this paper, we prove strong subconvexity bounds for self-dual $\mathrm{GL}(3)$ $L$-functions in the $t$-aspect and for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ $L$-functions in the $\mathrm{GL}(2)$-spectral aspect. The bounds are strong in…

For $L$-functions attached to automorphic representations of unitary groups $U_{n+1}\times U_n$, we establish a subconvex bound valid in certain horizontal aspects, where the set of ramified places is allowed to vary.

We study the average of the product of the central values of two $L$-functions of modular forms $f$ and $g$ twisted by Dirichlet characters to a large prime modulus $q$. As our principal tools, we use spectral theory to develop bounds on…

In this paper, we prove the smooth cubic moments vanish for the Hecke--Maass cusp forms, which gives a new case of the random wave conjecture. In fact, we can prove a polynomial decay for the smooth cubic moments, while for the smooth…

We establish an asymptotic formula with a power-saving error term for the twisted mixed moment of Dirichlet $L$-functions and automorphic $L$-functions twisted by all primitive characters modulo $q$, valid for all admissible moduli. As a…

We obtain the formula for the twisted harmonic second moment of the $L$-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the…

We improve upon the local bound in the depth aspect for sup-norms of newforms on $D^\times$ where $D$ is an indefinite quaternion division algebra over $\mathbb{Q}$. Our sup-norm bound implies a depth-aspect subconvexity bound for $L(1/2, f…

We show that if one can compute a little more than a particular moment for some family of L-functions, then one has upper bounds of the conjectured order of magnitude for all smaller (positive, real) moments and a one-sided central limit…

The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith, there are now precise conjectures for their limiting values. We develop a simple method to establish…

We prove that the fourth moment of holomorphic Hecke cusp forms is bounded provided that the Riemann Hypothesis holds for an appropriate degree 8 L-function. We accomplish this using Watson's formula, which translates the question in hand…

Let $1\le N<M$ with $N$ and $M$ coprime and square-free. Through classical analytic methods we estimate the first moment of central $L$-values $ L(1/2,f\times g) $ where $f\in S^*_k(N)$ runs over primitive holomorphic forms of level $N$ and…

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over…