on Selberg trace formula
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The selberg trace formula has two forms: one is for a setting of a semi simple group $G$ and its cocompact subgroup $Gamma$, and relates the geometric and spectral side of the canonical automorphic representation of $G$, which is normally we are talking about, another is for a Laplacian operator on a Riemannian surface, and relates the spectrum of it with the length of geodesic curves, which seems not a special case of the first form, although of course they have much similarity. I am just wondering if the second form can be reduced from the first form, what is the relation of them?
modular-forms laplacian geodesic automorphic-forms
asked Sep 5 at 10:34
abc
581413
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up vote
1
down vote
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The selberg trace formula has two forms: one is for a setting of a semi simple group $G$ and its cocompact subgroup $Gamma$, and relates the geometric and spectral side of the canonical automorphic representation of $G$, which is normally we are talking about, another is for a Laplacian operator on a Riemannian surface, and relates the spectrum of it with the length of geodesic curves, which seems not a special case of the first form, although of course they have much similarity. I am just wondering if the second form can be reduced from the first form, what is the relation of them?
modular-forms laplacian geodesic automorphic-forms
asked Sep 5 at 10:34
abc
581413
Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The selberg trace formula has two forms: one is for a setting of a semi simple group $G$ and its cocompact subgroup $Gamma$, and relates the geometric and spectral side of the canonical automorphic representation of $G$, which is normally we are talking about, another is for a Laplacian operator on a Riemannian surface, and relates the spectrum of it with the length of geodesic curves, which seems not a special case of the first form, although of course they have much similarity. I am just wondering if the second form can be reduced from the first form, what is the relation of them?
modular-forms laplacian geodesic automorphic-forms
asked Sep 5 at 10:34
abc
581413
The selberg trace formula has two forms: one is for a setting of a semi simple group $G$ and its cocompact subgroup $Gamma$, and relates the geometric and spectral side of the canonical automorphic representation of $G$, which is normally we are talking about, another is for a Laplacian operator on a Riemannian surface, and relates the spectrum of it with the length of geodesic curves, which seems not a special case of the first form, although of course they have much similarity. I am just wondering if the second form can be reduced from the first form, what is the relation of them?
modular-forms laplacian geodesic automorphic-forms
modular-forms laplacian geodesic automorphic-forms
asked Sep 5 at 10:34
abc
581413
asked Sep 5 at 10:34
abc
581413
asked Sep 5 at 10:34
abc
581413
asked Sep 5 at 10:34
abc
581413
asked Sep 5 at 10:34
abc
581413
581413
Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58
add a comment |Â
Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58
Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58
Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58
add a comment |Â
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Are you asking if every Riemann surface is of the form $G/Gamma$? This is the uniformization theorem.
– Kimball
Sep 6 at 22:58