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Finite Monodromy and Artin Represent...

Lien, Emma,

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Finite Monodromy and Artin Representations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Finite Monodromy and Artin Representations // Emma Lien.
Author:	Lien, Emma,
Description:	1 electronic resource (69 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
Contained By:	Dissertations Abstracts International86-03B.
Subject:	Decomposition. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31315829
ISBN:	9798384211693

Finite Monodromy and Artin Representations /
Lien, Emma,

Finite Monodromy and Artin Representations /Emma Lien. - 1 electronic resource (69 pages)

Source: Dissertations Abstracts International, Volume: 86-03, Section: B.

Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the exact representation. On the Galois side, certain character sums related to hypergeometric functions have been shown to be related to infinite families of Artin representations, and through the manipulation of these sums we can relate certain cases to known automorphic representations.

English

ISBN: 9798384211693Subjects--Topical Terms:

3561186
Decomposition.

Finite Monodromy and Artin Representations /
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245 1 0 $a Finite Monodromy and Artin Representations / $c Emma Lien.
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500 $a Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
500 $a Advisors: Long, Ling.
502 $b Ph.D. $c Louisiana State University and Agricultural & Mechanical College $d 2024.
520 $a Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the exact representation. On the Galois side, certain character sums related to hypergeometric functions have been shown to be related to infinite families of Artin representations, and through the manipulation of these sums we can relate certain cases to known automorphic representations.
546 $a English
590 $a School code: 0107
650 4 $a Decomposition. $3 3561186
650 4 $a Mathematical functions. $3 3564295
650 4 $a Eigenvalues. $3 631789
650 4 $a Polynomials. $3 604754
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Louisiana State University and Agricultural & Mechanical College. $e degree granting institution. $3 3771841
720 1 $a Long, Ling $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-03B.
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792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31315829