2023-06-02T11:23:31Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00007042
2023-01-16T05:03:33Z
697:765:766
Functional relations and universality for several types of multiple zeta functions
Nakamura, Takashi
18975
中村, 隆
18976
名古屋大学
Nagoya University
博士(数理学)
Firstly, we prove a functional relation for the Tornheim double zeta function. Using this functional relation, we obtain simple proofs of some known formulas for special values of Tornheim and Euler-Zagier double zeta functions. Secondly, we obtain functional relations for Witten zeta functions by using a double L-values relation. By these functional relations, we obtain new proofs of known results on the Tornheim double zeta function, the Euler-Zagier double zeta function, their alternating and character analogues. Thirdly, we define λ-joint, a'-joint, (λ, λ)-joint, (λ, a')-joint and (a', a')-joint t-universality of Lerch zeta functions and consider the relations among those. Next we show the existence of (λ, λ)- joint t-universality. We also show the existence of λ-joint, a'-joint, (λ,a')-joint and (a',a')-joint t-universality by using inversion formulas. Fourthly, we show the following theorems. Suppose 0 < al < 1 are algebraically independent numbers and 0 < λl ≤ 1 for 1 ≤ l ≤ m. Then we have the joint t-universality for Lerch zeta functions L(λl,al,s) for 1 ≤ l ≤ m. Next we generalize Lerch zeta functions, and obtain the joint t-universality for them. In addition, we show examples of the non-existence of the joint t-universality for Lerch zeta functions and generalized Lerch zeta functions.
名古屋大学博士学位論文 学位の種類；博士（数理学）（課程） 学位授与年月日；平成19年6月29日
doctoral thesis
2007-06-29
application/pdf
甲第7607号
http://hdl.handle.net/2237/8718
https://nagoya.repo.nii.ac.jp/record/7042/files/ko-7607.pdf
eng