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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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Signs of Fourier coefficients of cusp form at sum of two squares
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2020Manish Kumar Pandey
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Normal-form analysis of the cusp-transcritical interaction: applications in population dynamics
Nonlinear Dynamics, 2020Petri Piiroinen, John Donohue
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Average behaviour of higher moments of cusp form coefficients
Functiones Et Approximatio, Commentarii Mathematici, 2022Guodong Hua
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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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