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.
5 Citations
Moments and oscillations of exponential sums related to cusp forms
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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…
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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
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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
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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
- Mathematics
- 2009
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
- Mathematics
- 1987
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
- Mathematics
- 2007
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
- Mathematics
- 2007
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
- Engineering
- 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…