On meromorphic continuation of local zeta functions

Joe Kamimoto, Toshihiro Nose

研究成果: 著書/レポートタイプへの貢献会議での発言

抄録

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.

元の言語英語
ホスト出版物のタイトルComplex Analysis and Geometry - KSCV 2014
編集者Jisoo Byun, Filippo Bracci, Hervé Gaussier, Kang-Tae Kim, Nikolay Shcherbina, Kengo Hirachi
出版者Springer New York LLC
ページ187-195
ページ数9
ISBN(印刷物)9784431557432
DOI
出版物ステータス出版済み - 1 1 2015
イベント10th Korean Conference on Several Complex Variables, KSCV 2014 - Gyeongju, 大韓民国
継続期間: 8 7 20148 11 2014

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
144
ISSN(印刷物)2194-1009
ISSN(電子版)2194-1017

その他

その他10th Korean Conference on Several Complex Variables, KSCV 2014
大韓民国
Gyeongju
期間8/7/148/11/14

Fingerprint

Meromorphic
Riemann zeta function
Continuation
Pole
Argand diagram
Singularity
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Kamimoto, J., & Nose, T. (2015). On meromorphic continuation of local zeta functions. : J. Byun, F. Bracci, H. Gaussier, K-T. Kim, N. Shcherbina, & K. Hirachi (版), Complex Analysis and Geometry - KSCV 2014 (pp. 187-195). (Springer Proceedings in Mathematics and Statistics; 巻数 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. 版 / 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; 巻 144).

研究成果: 著書/レポートタイプへの貢献会議での発言

Kamimoto, J & Nose, T 2015, On meromorphic continuation of local zeta functions. : J Byun, F Bracci, H Gaussier, K-T Kim, N Shcherbina & K Hirachi (版), Complex Analysis and Geometry - KSCV 2014. Springer Proceedings in Mathematics and Statistics, 巻. 144, Springer New York LLC, pp. 187-195, 10th Korean Conference on Several Complex Variables, KSCV 2014, Gyeongju, 大韓民国, 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. : Byun J, Bracci F, Gaussier H, Kim K-T, Shcherbina N, Hirachi K, 編集者, 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. 編集者 / 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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