Tables from this paper
69 Citations
Multiple gamma functions, multiple sine functions, and Appell’s O-functions
- Mathematics
- 2011
Kurokawa introduced q-multiple gamma functions and q-multiple sine functions. We show that the Appell’s O-function is expressed via the q-multiple gamma function. We also give some applications of…
Remarks on Shintani's zeta function
- Mathematics
- 2005
We introduce a zeta function attached to a represen- tation of a group. We show that the multi-dimensional zeta function due to Shintani (Sh1), which is a generalization of the multiple Hurwitz zeta…
Differential Algebraicity of Multiple Sine Functions
- Mathematics
- 2005
AbstractThe differential algebraicity of the multiple sine functions
$$S_{r} (x, \underline{\omega})$$ is investigated. The goal of the paper is to show the differential algebraicity of
$$S_{r} (x,…
Rozansky–Witten Theory, Localised Then Tilted
- MathematicsCommunications in Mathematical Physics
- 2022
The paper has two parts, in the first part, we apply the localisation technique to the Rozansky–Witten theory on compact hyperkähler targets. We do so via first reformulating the theory as some…
Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models
- Physics
- 2014
We develop Coulomb gas pictures of strong and weak coupling regimes of supersymmetric Yang-Mills theory in five and four dimensions. By relating them to the matrix models that arise in Chern-Simons…
The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps
- Mathematics
- 2009
In this paper, we study the Ruelle zeta function and the Selberg zeta functions attached to the fundamental representations for real hyperbolic manifolds with cusps. In particular, we show that they…
Some expressions of double and triple sine functions
- MathematicsSUT Journal of Mathematics
- 2007
. We show some expressions of double and triple sine functions. Then we apply the results to special values of Dirichlet L -functions and ζ (3).
Kronecker limit formula for real quadratic fields and Shintani invariant (Proceedings of the Symposium on Algebraic Number theory and Related Topics)
- Mathematics
- 2007
We report on a result on Shintanis ray class invariant obtained in [5]. §1. Shintani invariant Let K be a real quadratic field. We denote by Cl_{K}(\mathrm{f}) the narrow ray class group of K modulo…
Euler Product Expression of Triple Zeta Functions
- Mathematics
- 2005
We construct multiple zeta functions considered as absolute tensor products of usual zeta functions. We establish Euler product expressions for triple zeta functions $\zeta(s,\mathbb {F}_p)\otimes…
References
SHOWING 1-10 OF 26 REFERENCES
Bridgman Anvil with a Sintered Diamond Core for Phase Transformation Studies at High Pressures and High Temperatures
- Materials Science
- 1991
A new Bridgman anvil composed of tungsten carbide with a sintered diamond core is described. The truncated face of the anvil is 26mm in diameter, the central part of which consists of the sintered…
Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
- Mathematics
- 1956
In The following lectures we shall give a brief sketch of some representative parts of certain investigations that have been undertaken during the last five years. The center of these investigations…
Multiple Zeta Functions: An Example
- Mathematics
- 1992
up to a factor exp(P(s)) for a polynomial P(s). Here we simplify the notation by omitting the usual exponential factor making the convergence, since at the first level we are mainly interested in…
Gamma factors and Plancherel measures
- Mathematics
- 1992
We explicitly calculate gamma factors of Selberg zeta functions and give a neat formula to the associated Plancherel measures. This report supplements the previous one [7]. The details are described…
Multiple sine functions and Selberg zeta functions
- Mathematics
- 1991
We describe basic properties of multiple sine functions, and as an application, we report the calculation of the "gamma factors" of SelbergGangolli-Wakayama zeta functions of rank one locally…
Sur la détermination d’un système orthogonal complet dans un espace de riemann symétrique clos
- Mathematics
- 1929
Spectral functions, special functions and the Selberg zeta function
- Mathematics
- 1987
The functional determinant of an eigenvalue sequence, as defined by zeta regularization, can be simply evaluated by quadratures. We apply this procedure to the Selberg trace formula for a compact…
Determinants of Laplacians
- Mathematics
- 1987
The determinant of the Laplacian on spinor fields on a Riemann surface is evaluated in terms of the value of the Selberg zeta function at the middle of the critical strip. A key role in deriving this…