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  5. Explicit identities on zeta values over imaginary quadratic field
 
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Explicit identities on zeta values over imaginary quadratic field

Source
arXiv
Date Issued
2021-05-01
Author(s)
Banerjee, Soumyarup
Kumar, Rahul
Abstract
In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any totally real number field is quite well known in literature. In fact, in one of the famous article, Zagier obtained an explicit formula for Dedekind zeta function at point 2 and conjectured an identity at any even values over any number field. We here exhibit the identities for both even and odd values of the Dedekind zeta function over an imaginary quadratic field which are analogous to Ramanujan's identities for even and odd zeta values over $\Q$. Moreover, any complex zeta values over imaginary quadratic field may also be evaluated from our identities
URI
http://arxiv.org/abs/2105.04141
https://d8.irins.org/handle/IITG2025/20079
Subjects
Number Theory
Classical Analysis
ODE
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