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  Mod-2 dihedral Galois representations of prime conductor

Kedlaya, K. S., & Medvedovsky, A. (2019). Mod-2 dihedral Galois representations of prime conductor. In R. Scheidler, & J. Sorenson (Eds.), Proceedings of the Thirteenth Algorithmic Number Theory Symposium (pp. 325-342). Berkeley: Mathematical Sciences Publishers.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-8A7C-6 Version Permalink: https://hdl.handle.net/21.11116/0000-000B-1C32-E
Genre: Conference Paper

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Kedlaya-Medvedovsky_Mod-2 dihedral Galois representations of prime conductor_2019.pdf (Publisher version), 3MB
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https://doi.org/10.2140/obs.2019.2.325 (Publisher version)
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 Creators:
Kedlaya, Kiran S., Author
Medvedovsky, Anna1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Algebraic Geometry
 Abstract: For all odd primes N up to 500000, we compute the action of the Hecke operator T_2 on the space S_2(Gamma_0(N), Q) and determine whether or not the reduction mod 2 (with respect to a suitable basis) has 0 and/or 1 as eigenvalues. We then partially explain the results in terms of class field theory and modular mod-2 Galois representations. As a byproduct, we obtain some nonexistence results on elliptic curves and modular forms with certain mod-2 reductions, extending prior results of Setzer, Hadano, and Kida.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 22
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1806.04653
DOI: 10.2140/obs.2019.2.325
URI: http://arxiv.org/abs/1806.04653
 Degree: -

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Title: Thirteenth International Algorithmic Number Theory Symposium
Place of Event: Madison, Wis.
Start-/End Date: 2018-07-16 - 2018-07-20

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Title: Proceedings of the Thirteenth Algorithmic Number Theory Symposium
Source Genre: Proceedings
 Creator(s):
Scheidler, Renate , Editor
Sorenson, Jonathan , Editor
Affiliations:
-
Publ. Info: Berkeley : Mathematical Sciences Publishers
Pages: x, 478 Volume / Issue: - Sequence Number: - Start / End Page: 325 - 342 Identifier: DOI: 10.2140/obs.2019.2-1
ISBN: 978-1-935107-02-6
ISBN: 978-1-935107-03-3

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Title: Open Book Series
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Pages: - Volume / Issue: 2 Sequence Number: - Start / End Page: - Identifier: -