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Darrin Doud

214 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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Even icosahedral Galois representations with prime conductor

with Michael W. Moore
Journal of Number Theory, 118:1 (2006) 62-70.

Abstract: In this paper, we use a series of targeted Hunter searches to prove that the minimal prime conductor of an even icosahedral Galois representation is 1951. In addition, we give a complete list of all prime conductors less than 10,000 of even icosahedral Galois representations.

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Cited in

• Andrew Booker and Andreas Strombergsson, Numerical computations with the trace formula and the Selberg eigenvalue conjecture, Journal fur die reine und angewandte Mathematik, 607 (2007), 113--161.
• John Jones and David Roberts, Number fields ramified at one prime, in Algorithmic Number Theory, Lecture Notes in Computer Science volume 5011, 2008, 226-239.
• Meghan DeWitt and Darrin Doud, Finding Galois representations corresponding to certain Hecke eigenclasses, Int. J. Number Theory, 5 (2009), 1-11.
• Nigel Boston and Nadya Markin, The fewest primes ramified in a $G$-extension of Q, Ann. Sci. Math. Quebec, 33 (2009), 145-154.
• Jared Weinstein, Reciprocity laws and Galois representations: recent breakthroughs, Bull. Amer. Math. Soc. (N.S.) 53 (2016), 1-39.
• Andrew R. Booker, Min Lee, and Andreas Strombergsson, Twist-minimal trace formulas and the Selberg eigenvalue conjecture, ArXiv preprint, 2018.