Eisenstein Metrics
We study families of metrics on automorphic vector bundles associated to representations of the modular group. These metrics are defined using an Eisenstein series construction. We show that in certain cases, the residue of these Eisenstein metrics at their rightmost pole is a harmonic metric for th...
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| creator | Franc, Cameron |
| description | We study families of metrics on automorphic vector bundles associated to
representations of the modular group. These metrics are defined using an
Eisenstein series construction. We show that in certain cases, the residue of
these Eisenstein metrics at their rightmost pole is a harmonic metric for the
underlying representation of the modular group. The last section of the paper
considers the case of a family of representations that are indecomposable but
not irreducible. The analysis of the corresponding Eisenstein metrics, and the
location of their rightmost pole, is an open question whose resolution depends
on the asymptotics of matrix-valued Kloosterman sums. |
| doi_str_mv | 10.48550/arxiv.2108.04120 |
| format | Article |
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representations of the modular group. These metrics are defined using an
Eisenstein series construction. We show that in certain cases, the residue of
these Eisenstein metrics at their rightmost pole is a harmonic metric for the
underlying representation of the modular group. The last section of the paper
considers the case of a family of representations that are indecomposable but
not irreducible. The analysis of the corresponding Eisenstein metrics, and the
location of their rightmost pole, is an open question whose resolution depends
on the asymptotics of matrix-valued Kloosterman sums.</description><identifier>DOI: 10.48550/arxiv.2108.04120</identifier><language>eng</language><subject>Mathematics - Differential Geometry ; Mathematics - Number Theory</subject><creationdate>2021-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2108.04120$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2108.04120$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Franc, Cameron</creatorcontrib><title>Eisenstein Metrics</title><description>We study families of metrics on automorphic vector bundles associated to
representations of the modular group. These metrics are defined using an
Eisenstein series construction. We show that in certain cases, the residue of
these Eisenstein metrics at their rightmost pole is a harmonic metric for the
underlying representation of the modular group. The last section of the paper
considers the case of a family of representations that are indecomposable but
not irreducible. The analysis of the corresponding Eisenstein metrics, and the
location of their rightmost pole, is an open question whose resolution depends
on the asymptotics of matrix-valued Kloosterman sums.</description><subject>Mathematics - Differential Geometry</subject><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwkAQQNFtLCTa2FnpDyTO7DuliC-I2KQPk90NLGiQJIj-vRitbnc5jC0RMmmVgg11r_jMOILNQCKHKVvsYx_afgixXV_C0EXXz9ikoVsf5v8mrDzsy90pLa7H825bpKQNpHntuM-tl6jQcmtlE2RDaMCjy7VSQiNR40m73GhhDNRopAtCcA9kHIqErX7bEVU9unin7l19cdWIEx_XHjIr</recordid><startdate>20210809</startdate><enddate>20210809</enddate><creator>Franc, Cameron</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210809</creationdate><title>Eisenstein Metrics</title><author>Franc, Cameron</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-9bc2d98d415182884fe4fa170d1c9655361aafda6c9763770b174ce332d0a7c13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Differential Geometry</topic><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Franc, Cameron</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Franc, Cameron</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Eisenstein Metrics</atitle><date>2021-08-09</date><risdate>2021</risdate><abstract>We study families of metrics on automorphic vector bundles associated to
representations of the modular group. These metrics are defined using an
Eisenstein series construction. We show that in certain cases, the residue of
these Eisenstein metrics at their rightmost pole is a harmonic metric for the
underlying representation of the modular group. The last section of the paper
considers the case of a family of representations that are indecomposable but
not irreducible. The analysis of the corresponding Eisenstein metrics, and the
location of their rightmost pole, is an open question whose resolution depends
on the asymptotics of matrix-valued Kloosterman sums.</abstract><doi>10.48550/arxiv.2108.04120</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Differential Geometry Mathematics - Number Theory |
| title | Eisenstein Metrics |
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