# Averages of coefficients of a class of degree 3 L-functions

@article{Huang2021AveragesOC, title={Averages of coefficients of a class of degree 3 L-functions}, author={Bingrong Huang and Yongxiao Lin and Zhiwei Wang}, journal={The Ramanujan Journal}, year={2021}, volume={57}, pages={79-91} }

In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three L -functions which can be factorized as a product of a degree one and a degree two L -functions. We emphasize that we can break the 1/2-barrier in the error term, and we get an explicit exponent. Our proof relies on methods from the theory of exponential sums.

## 2 Citations

Uniform bounds for lattice point counting and partial sums of zeta functions

- MathematicsMathematische Zeitschrift
- 2021

We prove uniform versions of two classical results in analytic number theory.
The first is an asymptotic for the number of points of a complete lattice $\Lambda \subseteq \mathbb{R}^d$ inside the…

Analytic twists of $\rm GL_2\times\rm GL_2$ automorphic forms

- Mathematics
- 2019

Let f and g be holomorphic or Maass cusp forms for SL2(Z) with normalized Fourier coefficients λf (n) and λg(n), respectively. In this paper, we prove nontrivial estimates for the sum ∞

## References

SHOWING 1-10 OF 20 REFERENCES

Distribution of mass of holomorphic cusp forms

- Mathematics
- 2013

We prove an upper bound for the L^4-norm and for the L^2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form of large weight. The method is based on Watson's formula and…

Summation Formulae for Coefficients of L-functions

- MathematicsCanadian Journal of Mathematics
- 2005

Abstract With applications in mind we establish a summation formula for the coefficients of a general Dirichlet series satisfying a suitable functional equation. Among a number of consequences we…

Decoupling, exponential sums and the Riemann zeta function

- Mathematics
- 2014

We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as…

Bilinear forms with Kloosterman sums and applications

- Mathematics
- 2015

We prove non-trivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the Polya-Vinogradov range. We then derive applications to the second…

Analytic Number Theory

- Mathematics
- 2004

Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large…

Van der Corput's method of exponential sums

- Mathematics
- 1991

1. Introduction 2. The simplest Van Der Corput estimates 3. The method of exponent pairs 4. Application of exponent pairs 5. Computing optimal exponent pairs 6. Two dimensional exponential sums 7.…

Oscillatory integrals with uniformity in parameters

- MathematicsJournal de Théorie des Nombres de Bordeaux
- 2019

We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is…

Analytic Twists of GL3 × GL2 Automorphic Forms

- MathematicsInternational Mathematics Research Notices
- 2021

Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. Let $f$ be a holomorphic or Maass cusp form for…

A method in the theory of exponential sums

- Mathematics, Geology
- 1987

Means for emitting high-pressure jets of fluid such as water, and mechanical rock breaking wheels, are positioned on a rotary drill bit for cooperatively cutting an axially extending bore hole…