Pythagoras0: /* 메타데이터 */ 새 문단

2022-07-06T07:33:22Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2022-07-06T07:33:20Z

노트: 새 문단

새 문서

== 노트 ==

===말뭉치===
# 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.<ref name="ref_c2536028">[https://en.wikipedia.org/wiki/Selberg_trace_formula Selberg trace formula]</ref>
# Motivated by the analogy, Selberg introduced the Selberg zeta function of a Riemann surface, whose analytic properties are encoded by the Selberg trace formula.<ref name="ref_c2536028" />
# The original Selberg trace formula studied a discrete subgroup Γ of a real Lie group G(R) (usually SL 2 (R)).<ref name="ref_7e1b520d">[https://en.wikipedia.org/wiki/Arthur%E2%80%93Selberg_trace_formula Arthur–Selberg trace formula]</ref>
# The Arthur–Selberg trace formula can be used to study similar correspondences on higher rank groups.<ref name="ref_7e1b520d" />
# 1 we review the Selberg trace formula for compact quotient.<ref name="ref_fe8768fd">[http://www.claymath.org/library/cw/arthur/pdf/62.pdf Clay mathematics proceedings]</ref>
# The method is based on considering the differences among several Selberg trace formulas with different weights for the Hilbert modular group.<ref name="ref_3014596c">[https://www.sciencedirect.com/science/article/pii/S0022314X14002583 Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces ☆]</ref>
# Previous knowledge of the Selberg trace formula is not assumed.<ref name="ref_bac793a1">[https://link.springer.com/book/10.1007/BFb0077696 An Approach to the Selberg Trace Formula via the Selberg Zeta-Function]</ref>
# The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function.<ref name="ref_bac793a1" />
# 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.<ref name="ref_38066723">[https://alexjbest.github.io/aut-forms-arthur-selberg/sec-eichler-selberg.html AFAS The Eichler-Selberg trace formula]</ref>
# 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.<ref name="ref_ecaed601">[https://bookstore.ams.org/ulect-9 Lectures on the Arthur-Selberg Trace Formula]</ref>
# 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.<ref name="ref_7570ad7c">[https://www.goodreads.com/book/show/654329.Lectures_on_the_Arthur_Selberg_Trace_Formula_ Lectures on the Arthur-Selberg Trace Formula.]</ref>
# 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.<ref name="ref_a5b84254">[http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/shim-ps.pdf Shimura varieties and the selberg trace formula *]</ref>
# XXIX (1977) Shimura varieties and the Selberg trace formula 2 If we follow this suggestion, we might divide the problem into three parts.<ref name="ref_a5b84254" />
# The Selberg trace formula is the way to do this.<ref name="ref_8cb2957f">[https://people.brandeis.edu/~rahulkrishna/NotesontheTF.pdf Notes on the trace formula]</ref>
===소스===
<references />

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	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q3077649 Q3077649]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'selberg'}, {'LOWER': 'trace'}, {'LEMMA': 'formula'}]

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Pythagoras0: /* 메타데이터 */ 새 문단

Pythagoras0: /* 노트 */ 새 문단