Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 6)
Lattice Methods for Algebraic Modular Forms on Classical Groups
We use Kneser’s neighbor method and isometry testing for lattices due to Plesken and Souveigner to compute systems of Hecke eigenvalues associated to definite forms of classical reductive algebraic groups.
KeywordsModular Form Hermitian Form Elementary Divisor Theta Series Automorphic Representation
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- [Chi]S. Chisholm, Lattice methods for algebraic modular forms on quaternionic unitary groups. Ph.D. thesis, University of Calgary. Anticipated 2013 Google Scholar
- [Eic75]M. Eichler, Correction to: “The basis problem for modular forms and the traces of the Hecke operators”, in Modular Functions of One Variable, IV, Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972. Lecture Notes in Math., vol. 476 (Springer, Berlin, 1975), pp. 145–147 Google Scholar
- [HPS89]H. Hijikata, A.K. Pizer, T.R. Shemanske, The Basis Problem for Modular Forms on Γ 0(N) (Amer. Math. Soc., Providence, 1989) Google Scholar
- [Koh01]D. Kohel, Hecke module structure of quaternions, in Class Field Theory: Its Centenary and Prospect, Tokyo, 1998, ed. by K. Miyake. Adv. Stud. Pure Math. vol. 30 (Math. Soc. Japan, Tokyo, 2001), pp. 177–195 Google Scholar
- [Loe]D. Loeffler, Computing with algebraic automorphic forms (this volume). doi: 10.1007/978-3-319-03847-6_2
- [Schu91]R. Schulze-Pillot, An algorithm for computing genera of ternary and quaternary quadratic forms, in Proc. Int. Symp. on Symbolic and Algebraic Computation, Bonn (1991) Google Scholar
- [vLCL92]M.A.A. van Leeuwen, A.M. Cohen, B. Lisser, LiE, a package for Lie group computations. CAN, Amsterdam, 1992 Google Scholar
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