| 1. |
- Axelson, Olav, 1937-, et al.
(författare)
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Regulatory toxicology and pharmacology.
- 2003
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Ingår i: International journal of occupational and environmental health. - 1077-3525 .- 2049-3967. ; 9, s. 386-389
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Tidskriftsartikel (refereegranskat)
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| 2. |
- Beckwith, Olivia, et al.
(författare)
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Congruences of Hurwitz class numbers on square classes
- 2022
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 409
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Tidskriftsartikel (refereegranskat)abstract
- We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us to establish Ramanujan-type congruences for Hurwitz class numbers on square classes, where the holomorphic case parallels previous work by Radu on partition congruences. We offer two applications. The first application demonstrates common divisibility features of Ramanujan-type congruences for Hurwitz class numbers. The second application provides a dichotomy between congruences for class numbers of imaginary quadratic fields and Ramanujan-type congruences for Hurwitz class numbers.
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| 3. |
- Beckwith, Olivia, et al.
(författare)
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Imaginary Quadratic Fields With ℓ-Torsion-Free Class Groups and Specified Split Primes
- 2024
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Ingår i: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - 1073-7928 .- 1687-0247.
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Tidskriftsartikel (refereegranskat)abstract
- Given an odd prime $\ell $ and finite set of odd primes $S_{+}$ , we prove the existence of an imaginary quadratic field whose class number is indivisible by $\ell $ and which splits at every prime in $S_{+}$ . Notably, we do not require that $p \not \equiv -1 \,\;(\mathrm{mod}\, \ell )$ for any of the split primes $p$ that we impose. Our theorem is in the spirit of a result by Wiles, but we introduce a new method. It relies on a significant improvement of our earlier work on the classification of non-holomorphic Ramanujan-type congruences for Hurwitz class numbers.
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| 4. |
- Bringmann, Kathrin, et al.
(författare)
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Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition
- 2015
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 367:9, s. 6647-6670
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Tidskriftsartikel (refereegranskat)abstract
- Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities which includes the real-analytic Jacobi forms from Zwegers’s PhD thesis. We provide several structure results for the space of such Jacobi forms, and we employ Zwegers’s μ-functions to establish a theta-like decomposition.
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| 5. |
- Raum, Martin, 1985, et al.
(författare)
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The structure of Siegel modular forms modulo pp and U(p) congruences
- 2015
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Ingår i: Mathematical Research Letters. - 1073-2780 .- 1945-001X. ; 22:3, s. 899-928
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Tidskriftsartikel (refereegranskat)abstract
- We determine the ring structure of Siegel modular forms of degree gg modulo a prime pp, extending Nagaoka’s result in the case of degree g=2g=2. We characterize U(p)U(p) congruences of Jacobi forms and Siegel modular forms, and surprisingly find different behaviors of Siegel modular forms of even and odd degrees.
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| 6. |
- Westerholt-Raum, Martin, 1985, et al.
(författare)
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Sturm bounds for Siegel modular forms
- 2015
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Ingår i: Research in Number Theory. - : Springer Science and Business Media LLC. - 2363-9555. ; 1:1
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Tidskriftsartikel (refereegranskat)abstract
- We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properties of specializations of Jacobi forms to torsion points. In particular, our approach is completely different from the proofs of the previously known cases g=1,2, which do not extend to the case of general g.
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