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5 results on '"Cusp form"'

3. Mean values connected with the Dedekind zeta-function of a non-normal cubic field

Author

Guangshi Lü

Subjects
Pure mathematics, 11f30, General Mathematics, 11f66, number field, dedekind zeta function, Algebraic number field, Cusp form, 11n37, Number theory, Norm (mathematics), QA1-939, Non normality, Dedekind cut, Cubic field, Dedekind zeta function, cusp form, Mathematics, 11r42
Abstract

After Landau’s famous work, many authors contributed to some mean values connected with the Dedekind zetafunction. In this paper, we are interested in the integral power sums of the coefficients of the Dedekind zeta function of a non-normal cubic extension K 3/ℚ, i.e. $$ S_{l,K_3 } (x) = \sum\nolimits_{m \leqslant x} {M^l (m)} $$, where M(m) denotes the number of integral ideals of the field K 3 of norm m and l ∈ ℕ. We improve the previous results for $$ S_{2,K_3 } (x) $$ and $$ S_{3,K_3 } (x) $$.

Published
2013

4. On zeta-functions associated to certain cusp forms. II

Author

Joern Steuding, Antanas Laurinčikas, and Darius Šiaučiūnas

Subjects
Cusp (singularity), Pure mathematics, General Mathematics, Mean value, Multiplicative function, Mathematical analysis, multiplicative function, Cusp form, 11m37, Continuation, Number theory, normalized hecke eigen form, QA1-939, 11m41, Algebra over a field, Hecke operator, Mathematics
Abstract

A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].

Published
2009

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