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On a two-variable zeta function for number fields

Lagarias, Jeffrey C. and Rains, Eric (2003) On a two-variable zeta function for number fields. Annales de l'Institut Fourier, 53 (1). pp. 1-68. ISSN 1777-5310.

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Recently van der Geer and Schoof [11, Prop. 1] formulated an “exact” analogue of the Riemann-Roch theorem for an algebraic number field K, based on Arakelov divisors. They used this result to formally express the completed zeta function ζ_K(s) of K as an integral over the Arakelov divisor class group Pic(K) of K. They introduced a two-variable zeta function attached to a number field K, also given as an integral over the Arkelov class group, which we call either the Arakelov zeta function or the two-variable zeta function. This zeta function was modelled after a two-variable zeta function attached to a function field over a finite filed, introduced in 1996 by Pellikaan [18]. For convenience we review the Arakelov divisor interpretation of the two-variable zeta function and the Riemann-Roch theorem for number fields in an appendix.

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Additional Information:© 2003 Association des Annales de l'Institut Fourier. Received September 24, 2001; accepted April 25, 2002. Work done in part during a visit to the Institute of Advanced Study.
Subject Keywords:Arakelov divisors, functional equation, infinitely divisible distributions, zeta functions
Issue or Number:1
Classification Code:MSC: 11M41, 11G40, 60E07
Record Number:CaltechAUTHORS:20171027-085620532
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82725
Deposited By: Tony Diaz
Deposited On:27 Oct 2017 16:23
Last Modified:03 Oct 2019 18:57

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