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Displaying similar documents to “On the average number of direct factors of finite abelian groups”

On Siegel's zero

D. M. Goldfeld, A. Schinzel (1975)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On sums of Hecke series in short intervals

Aleksandar Ivić (2001)

Journal de théorie des nombres de Bordeaux

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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 .