.
Shintani zeta function
In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were first studied by Takuro Shintani (1976). They include Hurwitz zeta functions, Barnes zeta functions, and Witten zeta functions as special cases.
Definition
The Shintani zeta function of \( (s_1, ..., sk_) \) is given by
\( \sum_{n_1,\dots,n_m\ge 0}\frac{1}{L_1^{s_1} \cdots L_k^{s_k}} \)
where each Lj is an inhomogeneous linear function of \( (n_1, ... ,n_m) \). The special case when k = 1 is the Barnes zeta function.
References
Yukie, Akihiko (1993), Shintani zeta functions, London Mathematical Society Lecture Note Series, 183, Cambridge University Press, ISBN 978-0-521-44804-8, MR1267735
Hida, Haruzo (1993), Elementary theory of L-functions and Eisenstein series, London Mathematical Society Student Texts, 26, Cambridge University Press, ISBN 978-0-521-43411-9, MR1216135
Shintani, Takuro (1976), "On evaluation of zeta functions of totally real algebraic number fields at non-positive integers", Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics 23 (2): 393–417, ISSN 0040-8980, MR0427231
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
