- C. Consani and J. Scholten. "Arithmetic on a Quintic Threefold." International Journal of Mathematics 12:8 (2001), 943–972.
- J. H. Conway and N. Sloane. Sphere Packings, Lattices and Groups, Second edition. New York: Springer Verlag, 1993.
- H. Darmon. "Rigid Local Systems, Hilbert Modular Forms, and Fermat's Last Theorem." Duke Math. J. 102:3 (2000), 413–449.
- L. Dembélé. "Explicit Computations of Hilbert Modular Forms on ℚ(√5)." PhD diss., McGill University. Available from World Wide Web (www.math.mcgill.ca/~darmon), 2002.
- D. Flath. "Decomposition of Representations into Tensor Products." Proc. Sympos. Pure Math., Part I 33 (1979), 179–183.
- G. van der Geer. Hilbert Modular Surfaces. New York: Springer-Verlag, 1988.
- S. S. Gelbart. Automorphic Forms on Adele Groups, Annals of Mathematics Studies, 83. Princeton, NJ: Princeton Univ. Press, 1975.
- H. Jacquet and R. P. Langlands. Automorphic Forms on GL(2), Lecture Notes in Math., 114. Berlin: Springer-Verlag, 1970.
- Kamal Khuri-Makdisi. "On the Curves Associated to Certain Rings of Automorphic Forms." Canad. J. Math. 53:1 (2001), 98–121.
- O. Körner. "Traces of Eichler-Brandt Matrices and Type Numbers of Quaternion Orders." Proc. Indian. Acad. Sci. 97 (1987), 187–199.
- Robert P. Langlands. Base Change for GL(2), Annals of Mathematics Studies, 96. Princeton, NJ: Princeton University Press, and Tokyo: University of Tokyo Press, 1980.
- Takayuki Oda. Periods of Hilbert Modular Surfaces, Progress in Mathematics, 19. Boston, MA: Birkhuser, 1982.
- Arnold Pizer. "An Algorithm for Computing Modular Forms on Γ0(N)." J. Algebra 64:2 (1980), 340–390.
- Jean-Pierre Serre. "Sur les représentations modulaires de degré 2 de Gal(ℚ̄/ℚ)." Duke Math. J. 54:1 (1987), 179–230.
- Jean-Pierre Serre. "Travaux de Wiles (et Taylor, …), I." Séminaire Bourbaki, Vol. 1994/95. Astérisque 237:803 (1996), 319–332.
- Jean-Pierre Serre. Abelian l-Adic Representations and Elliptic Curves, Research Notes in Mathematics, 7. Wellesley, MA: A K Peters, Ltd., 1997.
- N. Shepherd-Barron and R. Taylor. "Mod 2 and Mod 5 Icosahedral Representations." J.A.M.S. 10 (1997) 283–298.
- G. Shimura. Introduction to the Arithmetic Theory of Automorphic Functions. Princeton, NJ: Princeton Univ. Press 1971.
- G. Shimura. "The Special Values of the Zeta Functions Associated to Hilbert Modular Forms." Duke Math. J. 45:3 (1978), 637–679.
- C. M. Skinner and A. J. Wiles. "Residually Reducible Representations and Modular Forms." Inst. Hautes Études Sci. Publ. Math. 89 (1999), 5–126.
- C. M. Skinner and A. J. Wiles. "Nearly Ordinary Deformations of Irreducible Residual Representations." Ann. Fac. Sci. Toulouse Math. 6:1 (2001), 185–215.
- J. T. Socrates and D. Whitehouse. "Unramified Hilbert Modular Forms with Examples Relating to Elliptic Curves." Pacific Journal of Mathematics 219:2 (2005), 333–364.
- R. Taylor. "On Galois Representations Associated to Hilbert Modular Forms." Invent. Math. 98 (1988), 265–280.
- J. Tunnell. "Artin's Conjecture for Representations of Octahedral Type." Bull. Amer. Math. Soc. (N.S.) 5:2 (1981), 173–175.
- A. Wiles. "Modular Elliptic Curves and Fermat's Last Theorem." Annals of Maths. 141 (1995), 443–551.
Explicit Computations of Hilbert Modular Forms on ℚ(√5)
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