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On the distribution of the coefficients of the Dedekind zeta function over a certain sequence of positive integers

Matrapu S. Datt, Ekta Soni and Ayyadurai Sankaranarayanan
Vol. 15 (2026), No. 3, 159–179
DOI: 10.2140/cnt.2026.15.159
Abstract

Let 𝕂 be a nonnormal algebraic number field of cubic degree given by the polynomial x3 + ax2 + bx + c of discriminant D𝕂 < 0. We study the asymptotic formulae for the sums

∑ n=∑ i=16n i2≤x (n1,n2,n3,n4,n5,n6)∈ℤ6 a𝕂2(n) and ∑ n=∑ i=16n i2≤x (n1,n2,n3,n4,n5,n6)∈ℤ6 a𝕂3(n),

where a𝕂(n) is number of integral ideals of norm n and we improve the earlier known error terms.

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Keywords
Dedekind zeta function, Hecke eigenforms, normalized Fourier coefficient, symmetric square $L$-function, Dirichlet character
Mathematical Subject Classification
Primary: 11F11, 11F30, 11M06, 11R42
Milestones
Received: 17 January 2026
Revised: 19 March 2026
Accepted: 21 April 2026
Published: 30 May 2026
Authors
Matrapu S. Datt
School of Mathematics and Statistics
University of Hyderabad
Hyderabad
India
Ekta Soni
School of Mathematics and Statistics
University of Hyderabad
Hyderabad
India
Ayyadurai Sankaranarayanan
School of Mathematics and Statistics
University of Hyderabad
Hyderabad
India
© 2026 MSP (Mathematical Sciences Publishers).