On meromorphic continuation of local zeta functions

Joe Kamimoto, Toshihiro Nose

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationComplex Analysis and Geometry - KSCV 2014
EditorsJisoo Byun, Filippo Bracci, Hervé Gaussier, Kang-Tae Kim, Nikolay Shcherbina, Kengo Hirachi
PublisherSpringer New York LLC
Pages187-195
Number of pages9
ISBN (Print)9784431557432
DOIs
Publication statusPublished - Jan 1 2015
Event10th Korean Conference on Several Complex Variables, KSCV 2014 - Gyeongju, Korea, Republic of
Duration: Aug 7 2014Aug 11 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume144
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other10th Korean Conference on Several Complex Variables, KSCV 2014
CountryKorea, Republic of
CityGyeongju
Period8/7/148/11/14

Fingerprint

Meromorphic
Riemann zeta function
Continuation
Pole
Argand diagram
Singularity
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Kamimoto, J., & Nose, T. (2015). On meromorphic continuation of local zeta functions. In J. Byun, F. Bracci, H. Gaussier, K-T. Kim, N. Shcherbina, & K. Hirachi (Eds.), Complex Analysis and Geometry - KSCV 2014 (pp. 187-195). (Springer Proceedings in Mathematics and Statistics; Vol. 144). Springer New York LLC. https://doi.org/10.1007/978-4-431-55744-9_13

On meromorphic continuation of local zeta functions. / Kamimoto, Joe; Nose, Toshihiro.

Complex Analysis and Geometry - KSCV 2014. ed. / Jisoo Byun; Filippo Bracci; Hervé Gaussier; Kang-Tae Kim; Nikolay Shcherbina; Kengo Hirachi. Springer New York LLC, 2015. p. 187-195 (Springer Proceedings in Mathematics and Statistics; Vol. 144).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kamimoto, J & Nose, T 2015, On meromorphic continuation of local zeta functions. in J Byun, F Bracci, H Gaussier, K-T Kim, N Shcherbina & K Hirachi (eds), Complex Analysis and Geometry - KSCV 2014. Springer Proceedings in Mathematics and Statistics, vol. 144, Springer New York LLC, pp. 187-195, 10th Korean Conference on Several Complex Variables, KSCV 2014, Gyeongju, Korea, Republic of, 8/7/14. https://doi.org/10.1007/978-4-431-55744-9_13
Kamimoto J, Nose T. On meromorphic continuation of local zeta functions. In Byun J, Bracci F, Gaussier H, Kim K-T, Shcherbina N, Hirachi K, editors, Complex Analysis and Geometry - KSCV 2014. Springer New York LLC. 2015. p. 187-195. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-4-431-55744-9_13
Kamimoto, Joe ; Nose, Toshihiro. / On meromorphic continuation of local zeta functions. Complex Analysis and Geometry - KSCV 2014. editor / Jisoo Byun ; Filippo Bracci ; Hervé Gaussier ; Kang-Tae Kim ; Nikolay Shcherbina ; Kengo Hirachi. Springer New York LLC, 2015. pp. 187-195 (Springer Proceedings in Mathematics and Statistics).
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