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Brigham Young University
Math Department

Darrin Doud

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

phone:(801)422-1204
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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 describe calculations which distinguish between two possibilities for Galois representations in examples given by Ash, Doud, and Pollack of a generalization of a conjecture of Serre. Our calculations allow us to strengthen the evidence for this conjecture.

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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.

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