TY - GEN
T1 - On meromorphic continuation of local zeta functions
AU - Kamimoto, Joe
AU - Nose, Toshihiro
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We investigate meromorphic continuation of local zeta functions and properties of their poles. In the real analytic case, local zeta functions can be meromorphically continued to the whole complex plane and, moreover, properties of the poles have been precisely investigated. However, in the only smooth case, the situation of meromorphic continuation is very different. Actually, there exists an example in which a local zeta function has a singularity different from poles. We give a sufficient condition for that the first finitely many poles samely appear as in the real analytic case and exactly investigate properties of the first pole.
AB - We investigate meromorphic continuation of local zeta functions and properties of their poles. In the real analytic case, local zeta functions can be meromorphically continued to the whole complex plane and, moreover, properties of the poles have been precisely investigated. However, in the only smooth case, the situation of meromorphic continuation is very different. Actually, there exists an example in which a local zeta function has a singularity different from poles. We give a sufficient condition for that the first finitely many poles samely appear as in the real analytic case and exactly investigate properties of the first pole.
UR - http://www.scopus.com/inward/record.url?scp=84950985930&partnerID=8YFLogxK
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U2 - 10.1007/978-4-431-55744-9_13
DO - 10.1007/978-4-431-55744-9_13
M3 - Conference contribution
AN - SCOPUS:84950985930
SN - 9784431557432
T3 - Springer Proceedings in Mathematics and Statistics
SP - 187
EP - 195
BT - Complex Analysis and Geometry - KSCV 2014
A2 - Byun, Jisoo
A2 - Bracci, Filippo
A2 - Gaussier, Hervé
A2 - Kim, Kang-Tae
A2 - Shcherbina, Nikolay
A2 - Hirachi, Kengo
PB - Springer New York LLC
T2 - 10th Korean Conference on Several Complex Variables, KSCV 2014
Y2 - 7 August 2014 through 11 August 2014
ER -