Q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function
スポンサーリンク
概要
- 論文の詳細を見る
A q-analogue q(s) of the Riemann zeta function (s) was studied in [Kaneko M., Kurokawa N. and Wakayama M.: A variation of Euler's approach to values of the Riemann zeta function. Kyushu J. Math. 57 (2003), 175192] via a certain q-series of two variables. We introduce in a similar way a q-analogue of the Dirichlet L-functions and make a detailed study of them, including some issues concerning the classical limit of q(s) left open in [Kaneko M., Kurokawa N. and Wakayama M.: A variation of Euler's approach to values of the Riemann zeta function. Kyushu J. Math. 57 (2003), 175192]. We also examine a crystal limit (i.e. q 0) behavior of q(s). The q-trajectories of the trivial and essential zeros of (s) are investigated numerically when q moves in (0, 1]. Moreover, conjectures for the crystal limit behavior of zeros of q(s), which predict an interesting distribution of trivial zeros and an analogue of the Riemann hypothesis for a crystal zeta function, are given. © Walter de Gruyter 2008.
- Walter de Gruyterの論文
- 2008-01-01
Walter de Gruyter | 論文
- Purification and characterisation of blarinasin, a new tissue kallikrein-like protease from the short-tailed shrew Blarina brevicauda: comparative studies with blarina toxin
- Coagulation-fibrinolysis is more enhanced in twin than in singleton pregnancies
- Pregnancy-induced antithrombin deficiency
- Significance of radical oxygen production in sorus development and zoospore germination in Saccharina japonica (Phaeophyceae)
- A case study examining backchannels in conversations between Japanese–British dyads