| 1. |
- Blackman, T. R., et al.
(författare)
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Spectral correspondences for Maass waveforms on quaternion groups
- 2016
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Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 158, s. 1-22
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Tidskriftsartikel (refereegranskat)abstract
- We prove that in most cases the Jacquet-Langlands correspondence between newforms for Hecke congruence groups and newforms for quaternion orders is a bijection. Our proof covers almost all cases where the Hecke congruence group is of cocompact type, i.e. when a bijection is possible. The proof uses the Selberg trace formula.
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| 2. |
- Bober, Jonathan, et al.
(författare)
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The highest lowest zero of general L-functions
- 2015
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Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 147, s. 364-373
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Tidskriftsartikel (refereegranskat)abstract
- Stephen D. Miller showed that, assuming the Generalized Riemann Hypothesis, every entire L-function of real archimedean type has a zero in the interval 12+it with -t0
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| 3. |
- Brzezinski, Juliusz, 1939, et al.
(författare)
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Smooth lattices over quadratic integers
- 2008
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 258:1, s. 161-184
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Tidskriftsartikel (refereegranskat)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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| 4. |
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| 5. |
- Farmer, David W., et al.
(författare)
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Maass Forms on GL(3) and GL(4)
- 2014
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Ingår i: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 22, s. 6276-6301
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Tidskriftsartikel (refereegranskat)abstract
- We describe a practical method for finding an L-function without first finding an associated underlying object. The procedure involves using the Euler product, the Ramanujan bound, and the approximate functional equation in a new way. No use is made of the functional equation of twists of the L-function. The method is used to find a large number of Maass forms on (SL 3,Z) and to give the first examples of Maass forms of higher level on GL(3), and on GL(4) and Sp(4).
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| 6. |
- Farmer, David W., et al.
(författare)
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Varieties via their L-functions
- 2019
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Ingår i: Journal of Number Theory. - : Elsevier BV. - 0022-314X .- 1096-1658. ; 196, s. 364-380
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Tidskriftsartikel (refereegranskat)abstract
- We describe a procedure for determining the existence, or non-existence, of an algebraic variety of a given conductor via an analytic calculation involving L-functions. The procedure assumes that the Hasse–Weil L-function of the variety satisfies its conjectured functional equation, with no assumption of an associated automorphic object or Galois representation. We demonstrate the method by finding the Hasse–Weil L-functions of all hyperelliptic curves of conductor less than 500.
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| 7. |
- Lemurell, Stefan, 1968
(författare)
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A spectral correspondence for Maaß waveforms
- 1999
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Ingår i: Geom. Funct. Anal.. - 1016-443X .- 1420-8970. ; 9:6, s. 1128-1155
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Tidskriftsartikel (refereegranskat)abstract
- Let O^1 be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order O in an indefinite quaternion division algebra over Q. Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for O^1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian defined on the Maass newforms for the Hecke congruence group Gamma_0(d), when d is the discriminant of the maximal order O. We also show the equality of the traces of certain Hecke operators defined on the Laplace eigenspaces for O^1 and the newforms of level d, respectively.
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| 8. |
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| 9. |
- Lemurell, Stefan, 1968
(författare)
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Deformations of Maass forms
- 2005
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Ingår i: Math. Comp.. ; 74:252, s. 1967-1982
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Tidskriftsartikel (refereegranskat)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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| 10. |
- Lemurell, Stefan, 1968
(författare)
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Genera of arithmetic Fuchsian groups
- 1998
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Ingår i: Acta Arith.. ; 86:2, s. 171-191
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Tidskriftsartikel (refereegranskat)abstract
- The fundamental invariant of a Riemann surface is its genus. In this paper, using arithmetical means, we calculate the genus of certain Riemann surfaces defined by unit groups in quaternion algebras.
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