---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/ArithmeticGeometry/LFunctions/bibliography.html"
source: "https://docs.magma-maths.org/ArithmeticGeometry/LFunctions/bibliography.md"
part: "Arithmetic Geometry"
chapter: "L-Functions"
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  - {"title": "L-Functions", "source": "index-lfunctions.md"}
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next: {"title": "Modular Arithmetic Geometry", "source": "../../ModularArithmeticGeometry/index-modular-arithmetic-geometry.md"}
---

# Bibliography

<a id="cite-motives94"></a>
- **[JKS94]** Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre, editors. *Motives*, volume 55 of Proceedings of Symposia in Pure Mathematics, Providence, RI, 1994. American Mathematical Society.
<a id="cite-armitage-root-number"></a>
- **[Arm71]** J. V. Armitage. Zeta functions with a zero at $s=1/2$. *Invent. Math.*, 15(3):199–205, 1971.
<a id="cite-buhler-schoen-top"></a>
- **[BST97]** J. Buhler, C. Schoen, and J. Top. Cycles, $L$-functions and triple products of elliptic curves. *J. Reine. Angew. Math.*, 492:93–133, 1997.
<a id="cite-cohen2"></a>
- **[Coh00]** Henri Cohen. *Advanced Topics in Computational Number Theory*. Springer, Berlin–Heidelberg–New York, 2000.
<a id="cite-consani-scholten"></a>
- **[CS01b]** C. Consani and J. Scholten. Arithmetic on a quintic threefold. *Internat. J. Math*, 12/8:943–972, 2001.
<a id="cite-deligne-rootnumber"></a>
- **[Del79]** P. Deligne. Valeurs de fonctions $L$ et périodes d'intégrales. *Proc. Symposia Pure Math.*, 33/2:313–346, 1979.
<a id="cite-dps2012"></a>
- **[DPS12]** L. Dieulefait, A. Pacetti, and M. Schütt. Modularity of the Consani-Scholten quintic. *Documenta Mathematica*, 17:953–987, 2012.
<a id="cite-dokcomputel"></a>
- **[Dok02]** Tim Dokchitser. ComputeL, pari package to compute motivic $L$-functions. http://www.maths.bris.ac.uk/$\sim$matyd/computel/, 2002.
<a id="cite-dok04"></a>
- **[Dok04]** Tim Dokchitser. Computing special values of motivic $L$-functions. *Experimental Mathematics*, 13(2):137–149, 2004.
<a id="cite-dummigan-martin-watkins"></a>
- **[DMW09]** N. Dummigan, P. Martin, and M. Watkins. Euler factors and local root numbers for symmetric powers of elliptic curves. *Pure and Appl. Math. Qu.*, 5(4):1311–1341, 2009.
<a id="cite-friedlander-root-number"></a>
- **[Fri76]** J. B. Friedlander. On the class numbers of certain quadratic extensions. *Acta Arith.*, 28(4):391–393, 1975/76.
<a id="cite-lavrik67"></a>
- **[Lav67]** A. F. Lavrik. An approximate functional equation for the Hecke zeta-function of an imaginary quadratic field. *Mat. Zametki*, 2:475–482, 1967.
<a id="cite-martin-watkins"></a>
- **[MW06]** P. Martin and M. Watkins. Symmetric powers of elliptic curve $L$-functions. In F. Hess, S. Pauli, and M. Pohst, editors, *Algorithmic Number Theory*, volume 4076 of Lecture Notes in Computer Science, 377–392. Springer, 2006.
<a id="cite-rohrlich-parkcity"></a>
- **[Roh11]** D. E. Rohrlich. Root Numbers. In K. Rubin C. Popescu and A. Silverberg, editors, *Arithmetic of $L$-functions*, volume 18 of IAS / Park City Math. Ser., pages 353–448. Amer. Math. Soc., 2011.
<a id="cite-serre-root-number"></a>
- **[Ser71]** J.-P. Serre. Conducteurs d'Artin des caractères réels. *Invent. Math.*, 14(3):173–183, 1971.
<a id="cite-serre63"></a>
- **[Ser65]** Jean-Pierre Serre. Zeta and $L$ functions. In *Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963)*, pages 82–92. Harper & Row, New York, 1965.
<a id="cite-emsnt1"></a>
- **[Sha95]** I. R. Shafarevich, editor. *Number theory I*. Volume 49 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin, 1995. Fundamental problems, ideas and theories, A translation of Number theory 1 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990, Translation edited by A. N. Parshin and I. R. Shafarevich.
<a id="cite-tollis97"></a>
- **[Tol97]** Emmanuel Tollis. Zeros of Dedekind zeta functions in the critical strip. *Math. Comp.*, 66(219):1295–1321, 1997.
<a id="cite-geemen-straten"></a>
- **[vGvS93]** B. van Geemen and D. van Straten. The cusp forms of weight $3$ on $\Gamma\sb 2(2,4,8)$. *Math. Comp.*, 61(204):849–872, 1993.