---
title: "Bibliography"
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source: "https://docs.magma-maths.org/ModularArithmeticGeometry/AlgebraicModularForms/bibliography.md"
part: "Modular Arithmetic Geometry"
chapter: "Algebraic Modular Forms"
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  - {"title": "Modular Arithmetic Geometry", "source": "../index-modular-arithmetic-geometry.md"}
  - {"title": "Algebraic Modular Forms", "source": "index-algebraic-modular-forms.md"}
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---

# Bibliography

<a id="cite-afilsv22"></a>
- **[AFI+22]** Eran Assaf, Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord, and John Voight. Definite orthogonal modular forms: computations, excursions, and discoveries. *Res. Number Theory*, 8(4):Paper No. 70, 32, 2022. URL: [https://doi.org/10.1007/s40993-022-00373-2](https://doi.org/10.1007/s40993-022-00373-2), [doi:10.1007/s40993-022-00373-2](https://doi.org/10.1007/s40993-022-00373-2).
<a id="cite-alrtv24"></a>
- **[ALR+24]** Eran Assaf, Watson Ladd, Gustavo Rama, Gonzalo Tornaría, and John Voight. A database of paramodular forms from quinary orthogonal modular forms. In *LuCaNT: LMFDB, computation, and number theory*, volume 796 of Contemp. Math., pages 243–259. Amer. Math. Soc., [Providence], RI, [2024] opyright 2024. URL: [https://doi.org/10.1090/conm/796/16004](https://doi.org/10.1090/conm/796/16004), [doi:10.1090/conm/796/16004](https://doi.org/10.1090/conm/796/16004).
<a id="cite-greenbergvoight14"></a>
- **[GV14]** Matthew Greenberg and John Voight. Lattice methods for algebraic modular forms on classical groups. In *Computations with modular forms*, volume 6 of Contrib. Math. Comput. Sci., pages 147–179. Springer, Cham, 2014. URL: [https://doi.org/10.1007/978-3-319-03847-6_6](https://doi.org/10.1007/978-3-319-03847-6_6), [doi:10.1007/978-3-319-03847-6\\\_6](https://doi.org/10.1007/978-3-319-03847-6\_6).
<a id="cite-gross"></a>
- **[Gro99]** Benedict H. Gross. Algebraic modular forms. *Israel J. Math.*, 113:61–93, 1999. URL: [https://doi.org/10.1007/BF02780173](https://doi.org/10.1007/BF02780173), [doi:10.1007/BF02780173](https://doi.org/10.1007/BF02780173).
<a id="cite-loeffler08"></a>
- **[Loe08]** David Loeffler. Explicit calculations of automorphic forms for definite unitary groups. *LMS J. Comput. Math.*, 11:326–342, 2008. URL: [https://doi.org/10.1112/S1461157000000620](https://doi.org/10.1112/S1461157000000620), [doi:10.1112/S1461157000000620](https://doi.org/10.1112/S1461157000000620).
<a id="cite-murphy"></a>
- **[Mur99]** Brian Murphy. *Polynomial selection for the number field sieve integer factorisation algorithm*. PhD thesis, Oxford University, 1999. http://web.comlab.ox.ac.uk/oucl/work/richard.brent/ftp/Murphy-thesis.ps.gz.
<a id="cite-nguyenstehle09low"></a>
- **[NS09b]** Phong Q. Nguyen and Damien Stehlé. Low-dimensional lattice basis reduction revisited. *ACM Trans. Algorithms*, 5(4):Art. 46, 48, 2009. URL: [https://doi.org/10.1145/1597036.1597050](https://doi.org/10.1145/1597036.1597050), [doi:10.1145/1597036.1597050](https://doi.org/10.1145/1597036.1597050).
<a id="cite-ramatornaria"></a>
- **[RT20]** Gustavo Rama and Gonzalo Tornaría. Computation of paramodular forms. In *ANTS XIV—Proceedings of the Fourteenth Algorithmic Number Theory Symposium*, volume 4 of Open Book Ser., 353–370. Math. Sci. Publ., Berkeley, CA, 2020. URL: [https://doi.org/10.2140/obs.2020.4.353](https://doi.org/10.2140/obs.2020.4.353), [doi:10.2140/obs.2020.4.353](https://doi.org/10.2140/obs.2020.4.353).