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On Cusp form Coefficients in Exponential Sums
The Quarterly Journal of Mathematics, 2001Let \(f(z)\) be a holomorphic cusp form of weight \(k\) for \(SL_{2}(\mathbb Z)\), and \(e(t)=e^{2 \pi i t}\). The function \(f(z)\) has a Fourier expansion \(f(z)= \sum_{n=1}^{\infty} a(n) n^{(k-1)/2}e(nz),\) where \(a(n) \ll n^{\varepsilon}\) for any \(\varepsilon > 0\), due to Deligne.
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SIEGEL CUSP MODULAR FORMS AND COHOMOLOGY
Mathematics of the USSR-Izvestiya, 1987A famous result in the classical theory of modular forms is the theorem of Eichler-Shimura [see e.g. \textit{G. Shimura}, J. Math. Soc. Japan 11, 291-311 (1959; Zbl 0090.055)]. It gives a relation between the space of cusp forms (for a Fuchsian group \(\Gamma\) of the first kind) and the cohomology of \(\Gamma\).
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On the Structure and Slopes of Drinfeld Cusp Forms
Experimental Mathematics, 2022Andrea Bandini, Maria Valentino
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On the Asymptotic Distribution of Fourier Coefficients of Cusp Forms
Bulletin of the Brazilian Mathematical Society, 2023Huafeng Liu
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General asymptotic formula of Fourier coefficients of cusp forms over sum of two squares
Journal of Number Theory, 2022exaly
On the interlacing of the zeros of certain Poincaré cusp forms
Journal of Mathematical Analysis and Applications, 2023exaly
Explicit subconvexity savings for sup-norms of cusp forms on PGLn(R)
Journal of Number Theory, 2020Nate Gillman
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An \(\Omega\)-result for the coefficients of cusp forms
1975Sei \(f\) eine Spitzenform (ungleich null) der Dimension \(- k\), \(k\ge 12\), zur Modulgruppe mit der Fourier-Entwicklung \(f(z) = \sum_{n=1}^\infty a(n)e^{2\pi inz}\), \(\Im z>0\). In enger Anlehnung an Ergebnisse und Beweise von \textit{R. A. Rankin} [Math. Ann.
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On the gaps in the Fourier expansion of cusp forms
Ramanujan Journal, 2008Alexandru Zaharescu, Emre Alkan
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