The approximate functional equation for a class of zeta-functions

Chandrasekharan, K.; Narasimhan, Raghavan

doi:10.1007/bf01343729

Cited by 129 publications

(68 citation statements)

References 7 publications

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“…where the constant factor on the right hand side is the residue of ζ(s; Q) at s = Following the lines of Chandrasekharan and Narasimhan [4] one can deduce from Lemma 3…”

Section: The Mean-square and Other Preliminariesmentioning

confidence: 85%

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On the value-distribution of Epstein zeta-functions

Steuding¹

2007

Publicacions Matemàtiques

132

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We investigate the value-distribution of Epstein zeta-functions ζ(s; Q), where Q is a positive definite quadratic form in n variables. We prove an asymptotic formula for the number of c-values, i.e., the roots of the equation ζ(s; Q) = c, where c is any fixed complex number. Moreover, we show that, in general, these c-values are asymmetrically distributed with respect to the critical line Re s = . This complements previous results on the zero-distribution [30].

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“…where the constant factor on the right hand side is the residue of ζ(s; Q) at s = Following the lines of Chandrasekharan and Narasimhan [4] one can deduce from Lemma 3…”

Section: The Mean-square and Other Preliminariesmentioning

confidence: 85%

“…However, we can show a bit more. Chandrasekharan and Narasimhan [4] obtained an approximate functional equation for a quite general class of zeta-functions. It is not difficult to deduce from their general result:…”

Section: The Mean-square and Other Preliminariesmentioning

confidence: 99%

On the value-distribution of Epstein zeta-functions

Steuding¹

2007

Publicacions Matemàtiques

132

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“…Chandrasekharan and Narasimhan [3] first considered the mean square value of M( ). They showed that if K is a Galois extension of Q of degree , then…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

Lü

2012

Open Mathematics

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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 K 3 ( ) = ≤ M ( ), where M( ) denotes the number of integral ideals of the field K 3 of norm and ∈ N. We improve the previous results for S 2 K 3 ( ) and S 3 K 3 ( ). MSC:11N37, 11F66, 11F30, 11R42

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“…where a n denotes the number of integral ideals in E with norm n. From Lemma 9 in [1], it is known that a n is a multiplicative function and satisfies…”

Section: Preliminariesmentioning

confidence: 99%

Number of solutions of certain congruences

Lü

2009

Acta Arith.

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The approximate functional equation for a class of zeta-functions

Cited by 129 publications

References 7 publications

On the value-distribution of Epstein zeta-functions

On the value-distribution of Epstein zeta-functions

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

Number of solutions of certain congruences

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