Skip to main content
main-content
Top

Hint

Swipe to navigate through the chapters of this book

2021 | OriginalPaper | Chapter

Computing Classical Modular Forms

Authors : Alex J. Best, Jonathan Bober, Andrew R. Booker, Edgar Costa, John E. Cremona, Maarten Derickx, Min Lee, David Lowry-Duda, David Roe, Andrew V. Sutherland, John Voight

Published in: Arithmetic Geometry, Number Theory, and Computation

Publisher: Springer International Publishing

share
SHARE

Abstract

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and modular forms database (LMFDB).
Literature
12.
18.
go back to reference Kevin Buzzard, Computing weight one modular forms over \(\mathbb {C}\) and \(\overline {\mathbb {F}}_p\), Computations with modular forms, Contrib. Math. Comput. Sci., vol. 6, Springer, Cham, 2014, 129–146. Kevin Buzzard, Computing weight one modular forms over \(\mathbb {C}\) and \(\overline {\mathbb {F}}_p\), Computations with modular forms, Contrib. Math. Comput. Sci., vol. 6, Springer, Cham, 2014, 129–146.
46.
go back to reference Erich Hecke, Mathematische Werke, Göttingen, Vandenhoeck & Ruprecht, 1959. MATH Erich Hecke, Mathematische Werke, Göttingen, Vandenhoeck & Ruprecht, 1959. MATH
49.
52.
go back to reference John W. Jones and David P. Roberts, Timing analysis of targeted Hunter searches, Algorithmic number theory (Portland, OR, 1998), Lecture Notes in Comput. Sci., vol. 1423, Springer, Berlin, 1998, 412–423. John W. Jones and David P. Roberts, Timing analysis of targeted Hunter searches, Algorithmic number theory (Portland, OR, 1998), Lecture Notes in Comput. Sci., vol. 1423, Springer, Berlin, 1998, 412–423.
56.
go back to reference David Lowry-Duda, Visualizing modular forms, J. S. Balakrishnan et al. (eds.), Arithmetic geometry, number theory, and computation, Simons symposia, Springer, Cham, 2021, 539–560. David Lowry-Duda, Visualizing modular forms, J. S. Balakrishnan et al. (eds.), Arithmetic geometry, number theory, and computation, Simons symposia, Springer, Cham, 2021, 539–560.
65.
go back to reference J.-F. Mestre, La méthode des graphes. Exemples et applications, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986), Nagoya Univ., Nagoya, 1986, 217–242. J.-F. Mestre, La méthode des graphes. Exemples et applications, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986), Nagoya Univ., Nagoya, 1986, 217–242.
68.
go back to reference Fumiyuki Momose, On the l- adic representations attached to modular forms, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 1, 89–109. MathSciNetMATH Fumiyuki Momose, On the l- adic representations attached to modular forms, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 1, 89–109. MathSciNetMATH
71.
go back to reference Modular functions of one variable IV, Proceedings of the International Summer School on Modular Functions of One Variable and Arithmetical Applications, RUCA, University of Antwerp, Antwerp, July 17–August 3, 1972, eds. Bryan J. Birch and Willem Kuyk, Lecture Notes in Math., vol. 476, Springer-Verlag, Berlin, 1975. Modular functions of one variable IV, Proceedings of the International Summer School on Modular Functions of One Variable and Arithmetical Applications, RUCA, University of Antwerp, Antwerp, July 17–August 3, 1972, eds. Bryan J. Birch and Willem Kuyk, Lecture Notes in Math., vol. 476, Springer-Verlag, Berlin, 1975.
95.
go back to reference Dave J. Tingley, Elliptic curves uniformized by modular functions, Ph.D. thesis, University of Oxford, 1975. Dave J. Tingley, Elliptic curves uniformized by modular functions, Ph.D. thesis, University of Oxford, 1975.
97.
go back to reference Hideo Wada, Tables of Hecke operators. I, Seminar on Modern Methods in Number Theory (Inst. Statist. Math., Tokyo, 1971), Paper No. 39, Inst. Statist. Math., Tokyo, 1971, 1–10. Hideo Wada, Tables of Hecke operators. I, Seminar on Modern Methods in Number Theory (Inst. Statist. Math., Tokyo, 1971), Paper No. 39, Inst. Statist. Math., Tokyo, 1971, 1–10.
Metadata
Title
Computing Classical Modular Forms
Authors
Alex J. Best
Jonathan Bober
Andrew R. Booker
Edgar Costa
John E. Cremona
Maarten Derickx
Min Lee
David Lowry-Duda
David Roe
Andrew V. Sutherland
John Voight
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-80914-0_4

Premium Partner