An unconditional asymptotic formula is obtained for the smoothed mean square of quadratic twists of Fourier coefficients of a modular form.
Bounds for Moments of Twisted Fourier coefficients of Modular Forms
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We establish upper bounds for shifted moments of modular $L$-functions to a fixed modulus as well as quadratic twists of modular $L$-functions under the generalized Riemann hypothesis. Our results are then used to establish bounds for moments of sums involving with Fourier coefficients of a given modular form twisted by Dirichlet characters.
citation-role summary
background 1
citation-polarity summary
fields
math.NT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Mean squares of quadratic twists of the Fourier coefficients of modular forms
An unconditional asymptotic formula is obtained for the smoothed mean square of quadratic twists of Fourier coefficients of a modular form.