셀베르그 대각합 공식

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말뭉치

1. Selberg worked out the non-compact case when G is the group SL(2, R); the extension to higher rank groups is the Arthur–Selberg trace formula.
2. Motivated by the analogy, Selberg introduced the Selberg zeta function of a Riemann surface, whose analytic properties are encoded by the Selberg trace formula.
3. The original Selberg trace formula studied a discrete subgroup Γ of a real Lie group G(R) (usually SL 2 (R)).
4. The Arthur–Selberg trace formula can be used to study similar correspondences on higher rank groups.
5. 1 we review the Selberg trace formula for compact quotient.
6. The method is based on considering the differences among several Selberg trace formulas with different weights for the Hilbert modular group.
7. Previous knowledge of the Selberg trace formula is not assumed.
8. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function.
9. It is more general, there is an (Eichler-)Selberg trace formula for general level \(N\text{.}\) Even more generally there is a Selberg trace formula for Maass forms of arbitrary level.
10. The Arthur-Selberg trace formula is an equality between two kinds of traces: the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations.
11. The Arthur-Selberg trace formula is an equality between two kinds of traces - the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations.
12. Shimura varieties and the Selberg trace formula * R.P. Langlands This paper is a report on work in progress rather than a description of theorems which have attained their nal form.
13. XXIX (1977) Shimura varieties and the Selberg trace formula 2 If we follow this suggestion, we might divide the problem into three parts.
14. The Selberg trace formula is the way to do this.