BROWSE

Related Researcher

Author's Photo

Jun, Byungheup
School of Natural Science
Research Interests

ITEM VIEW & DOWNLOAD

SPECIAL VALUES OF PARTIAL ZETA FUNCTIONS OF REAL QUADRATIC FIELDS AT NONPOSITIVE INTEGERS AND THE EULER-MACLAURIN FORMULA

Cited 0 times inthomson ciCited 0 times inthomson ci
Title
SPECIAL VALUES OF PARTIAL ZETA FUNCTIONS OF REAL QUADRATIC FIELDS AT NONPOSITIVE INTEGERS AND THE EULER-MACLAURIN FORMULA
Author
Jun, ByungheupLee, Jungyun
Issue Date
2016-11
Publisher
AMER MATHEMATICAL SOC
Citation
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.368, no.11, pp.7935 - 7964
Abstract
We compute the special values at nonpositive integers of the partial zeta function of an ideal of a real quadratic field in terms of the positive continued fraction of the reduced element defining the ideal. We apply the integral expression of the partial zeta value due to Garoufalidis-Pommersheim (2001) using the Euler-Maclaurin summation formula for a lattice cone associated to the ideal. From the additive property of Todd series w.r.t. the (virtual) cone decomposition arising from the positive continued fraction of the reduced element of the ideal, we obtain a polynomial expression of the partial zeta values with variables given by the coefficient of the continued fraction. We compute the partial zeta values explicitly for s = 0, -1, -2 and compare the result with earlier works of Zagier (1977) and Garoufalidis-Pommersheim (2001). Finally, we present a way to construct Yokoi-Byeon-Kim type class number one criterion for some families of real quadratic fields
URI
https://scholarworks.unist.ac.kr/handle/201301/20695
URL
http://www.ams.org/journals/tran/2016-368-11/S0002-9947-2016-06679-9/
DOI
10.1090/tran/6679
ISSN
0002-9947
Appears in Collections:
PHY_Journal Papers
Files in This Item:
There are no files associated with this item.

find_unist can give you direct access to the published full text of this article. (UNISTARs only)

Show full item record

qrcode

  • mendeley

    citeulike

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

MENU