Displaying similar documents to “Counting points of small height on elliptic curves”

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 .