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- Brzezinski, Juliusz, 1939, et al.
(author)
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Smooth lattices over quadratic integers
- 2008
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 258:1, s. 161-184
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Journal article (peer-reviewed)abstract
- We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of "standard" pieces of ranks 1-4 and covers the case of the discriminant of the real quadratic number field congruent to 1 modulo 8 for which a general construction was not known. © 2007 Springer-Verlag.
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| 2. |
- Lemurell, Stefan, 1968
(author)
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Deformations of Maass forms
- 2005
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In: Math. Comp.. ; 74:252, s. 1967-1982
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Journal article (peer-reviewed)abstract
- We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface S under deformation of the surface. Our calculations indicate that if the Teichmüller space of S is not trivial, then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissolves into a resonance whose constant term is uniformly a factor of 10^{8} smaller than a typical Fourier coefficient of the form. We give explicit examples of those deformations in several cases.
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| 3. |
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