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On arbitrary products of eigenforms

Arvind Kumar, Jaban Meher (2016)

Acta Arithmetica

We characterize all the cases in which products of arbitrary numbers of nearly holomorphic eigenforms and products of arbitrary numbers of quasimodular eigenforms for the full modular group SL₂(ℤ) are again eigenforms.

On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

We have K - G k j K + G α j H j 3 ( 1 2 ) ϵ G K 1 + ϵ for K ϵ G K , where α j = ρ j ( 1 ) 2 ( cosh π k j ) - 1 , and ρ j ( 1 ) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λ j = k j 2 + 1 4 to which the Hecke series H j ( s ) is attached. This result yields the new bound H j ( 1 2 ϵ k j 1 3 + ϵ .

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