Bilateral Lerch theta and theta star function and Quadrilateral Lerch zeta and zeta star functions

中村, 隆

doi:10.51094/jxiv.872

##article.authors##

中村, 隆東京理科大学教養教育研究院

DOI:

https://doi.org/10.51094/jxiv.872

キーワード:

functional equation、 modular relation、 theta functions、 zeta functions

抄録

In the present paper, we construct theta functions with two parameters $a,b \in {\mathbb{R}}$ which satisfy Jacobi's modular relation.
Moreover, we give zeta functions with two parameters $a,b \in {\mathbb{R}}$ which satisfy Riemann's functional equation by the theta functions with two parameters.

利益相反に関する開示

The authors have no conflicts of interest directly relevant to the content of this article.

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