scholarly journals Integral power sums of Hecke eigenvalues

2011 ◽  
Vol 150 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Y.-K. Lau ◽  
G.-S. Lü ◽  
J. Wu
Keyword(s):  
Power Sums ◽  
Hecke Eigenvalues ◽  
Integral Power

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

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Guangshi Lü
Keyword(s):  
Zeta Function ◽  
Mean Values ◽  
Power Sums ◽  
Dedekind Zeta Function ◽  
Integral Power ◽  
Cubic Field ◽  
Cubic Extension

AbstractAfter 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 $$ S_{3,K_3 } (x) $$.

scholarly journals Power sums of Hecke eigenvalues and application

2009 ◽  
Vol 137 (4) ◽  
pp. 333-344 ◽  
Author(s):  
J. Wu
Keyword(s):  
Power Sums ◽  
Hecke Eigenvalues

scholarly journals Power sums of Hecke eigenvalues of Maass cusp forms

2014 ◽  
Vol 36 (3) ◽  
pp. 439-453 ◽  
Author(s):  
J. Wu ◽  
Z. Xu
Keyword(s):  
Cusp Forms ◽  
Power Sums ◽  
Hecke Eigenvalues

A concise proof of a theorem on products of power sums

1978 ◽  
Vol 6 (1) ◽  
pp. 11-17 ◽  
Author(s):  
P. S. Dwyer ◽  
N. N. Mikhail ◽  
D. S. Tracy
Keyword(s):  
Power Sums

scholarly journals IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

2014 ◽  
Vol 60 (1) ◽  
pp. 19-36
Author(s):  
Dae San Kim
Keyword(s):  
Generating Function ◽  
Bernoulli Polynomials ◽  
Roots Of Unity ◽  
Integral Expression ◽  
Power Sums ◽  
Exponential Generating Function

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

scholarly journals Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Taekyun Kim ◽  
Seog-Hoon Rim ◽  
Byungje Lee
Keyword(s):  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Power Sums ◽  
Invariant Integral ◽  
Generalized Bernoulli Polynomials ◽  
Symmetric Properties

By the properties ofp-adic invariant integral onℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties ofp-adic invariant integral onℤp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.

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