Linearized product of two Riemann zeta functions

Banerjee, Debika; Mehta, Jay

doi:10.3792/pjaa.90.123

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2016

2021

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Cited by 3 publications

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“…Wilton's approach to prove Theorem A involves techniques of real and complex analysis. Recently, D. Banerjee and J. Mehta [1] gave an alternative proof of Theorem A using number theoretic approach, and a similar result for Hurwitz zeta functions appeared in [15]. In this paper, we obtain an analogous result to that of Theorem A in number fields.…”

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confidence: 53%

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An analogue of Wilton's formula and values of Dedekind zeta functions

Banerjee¹,

Chakraborty²,

Hoque³

2016

Preprint

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J. R. Wilton obtained a formula for the product of two Riemann zeta functions. This formula played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We find an analogous formula for the product of two Dedekind zeta functions and then use this formula to find closed form expressions for Dedekind zeta values attached to arbitrary real as well as quadratic number fields at any positive integer.

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confidence: 53%

“…Note that the closed form expression of Dedekind zeta function of real quadratic number field at odd positive integers can not be obtained from (4.5) as the expression of L(s, χ D K ) at odd positive integers is still not known. Let σ (1)…”

Section: A Work Of Zagiermentioning

confidence: 99%