• Corpus ID: 119311825

# On the mean square of short exponential sums related to cusp forms

@inproceedings{ErnvallHytonen2010OnTM,
title={On the mean square of short exponential sums related to cusp forms},
author={Anne-Maria Ernvall-Hytonen},
year={2010}
}
The purpose of the article is to estimate the mean square of a squareroot length exponential sum of Fourier coefficients of a holomorphic cusp form.
Moments and oscillations of exponential sums related to cusp forms
• Esa V. Vesalainen
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2016
Abstract We consider large values of long linear exponential sums involving Fourier coefficients of holomorphic cusp forms. The sums we consider involve rational linear twists e(nh/k) with
Exponential sums related to Maass forms
• Mathematics
Acta Arithmetica
• 2019
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of
Mean square estimate for relatively short exponential sums involving Fourier coefficients of cusp forms
when α ∈ R. This was an improvement over the classical result by Wilton [12]. By the Rankin-Selberg mean value theorem [10] this bound is the best possible in the general case, even though for some
A pr 2 01 5 Exponential Sums Related to Maass Forms
• Mathematics
• 2018
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of

## References

SHOWING 1-10 OF 10 REFERENCES
On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms
• Mathematics
• 2008
We improve known estimates for the linear exponential sums containing Fourier coefficients of holomorphic cusp forms and show that in some cases, our bound is actually sharp. We also briefly visit
A relation between Fourier coefficients of holomorphic cusp forms and exponential sums
We consider certain specific exponential sums related to holomor- phic cusp forms, give a reformulation for the Lehmer conjecture and prove that certain exponential sums of Fourier coefficients of
On exponential sums involving the Ramanujan function
AbstractLet τ(n) be the arithmetical function of Ramanujan, α any real number, and x≥2. The uniform estimate $$\mathop \Sigma \limits_{n \leqslant x} \tau (n)e(n\alpha ) \ll x^6 \log x$$ is a
On the mean square of the divisor function in short intervals
We provide upper bounds for the mean square integral $$\int_X^{2X}(\Delta_k(x+h) - \Delta_k(x))^2 dx \qquad(h = h(X)\gg1, h = o(x) {\roman{as}} X\to\infty)$$ where $h$ lies in a suitable range. For
Uniform Bound for Hecke L-Functions
• Mathematics
• 2005
Our principal aim in the present article is to establish a uniform hybrid bound for individual values on the critical line of Hecke $L$-functions associated with cusp forms over the full modular
On the divisor function and the Riemann zeta-function in short intervals
AbstractWe obtain, for Tε≤U=U(T)≤T1/2−ε, asymptotic formulas for \int_{T}^{2T}\Bigl(E(t+U)-E(t)\Bigr)^{2}{\mathrm{d}}{t},\qquad \int_{T}^{2T}\Bigl(\Delta (t+U)-\Delta
A method in the theory of exponential sums
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