On a two-variable zeta function for number fields
- Creators
- Lagarias, Jeffrey C.
- Rains, Eric
Abstract
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.
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.Attached Files
Published - AIF_2003__53_1_1_0.pdf
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Additional details
- Eprint ID
- 82725
- Resolver ID
- CaltechAUTHORS:20171027-085620532
- Created
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2017-10-27Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field