swMATH ID: 7249
Software Authors: http://www.lmfdb.org/acknowledgment
Description: Welcome to the LMFDB, the database of L-functions, modular forms, and related objects. These pages are intended to be a modern handbook including tables, formulas, links, references, etc. to very concrete objects, in particular specific L-functions and their sources. L-functions are ubiquitous in number theory and have applications to mathematical physics and cryptography. By an L-function, we generally mean a Dirichlet series with a functional equation and an Euler product, the simplest example being the Riemann zeta function. Two of the seven Clay Mathematics Million Dollar Millennium Problems deal with properties of these functions, namely the Riemann Hypothesis and the Birch and Swinnerton-Dyer Conjecture. L-functions arise from and encode information about a number of mathematical objects. It is necessary to exhibit these objects along with the L-functions themselves, since typically we need these objects to compute L-functions. In these pages you will see examples of L-functions coming from modular forms, elliptic curves, number fields, and Dirichlet characters, as well as more generally from automorphic forms, algebraic varieties, and Artin representations. In addition, the database contains details about these objects themselves. See the Map of LMFDB for descriptions of connections between these objects. For additional information, there is a useful collection of freely available online sources at http://www.numbertheory.org/ntw/lecture_notes.html. The subject of L-functions is very rich, with many interrelationships. Our goal is to describe the data in ways that faithfully exhibit these interconnections, and to offer access to the data as a means of prompting further exploration and discovery. We believe that the creation of this website will lead to the development and understanding of new mathematics.
Homepage: http://www.lmfdb.org/
Related Software: Magma; SageMath; PARI/GP; GitHub; ecdata; endomorphisms; OEIS; DLMF; GAP; QCI; Maple; Mathematica; Arb; GL(n)pack; MathOverflow; ecdegsets; DiscreteZOO; OpenDreamKit; FindStat; OMDoc
Referenced in: 168 Publications
all top 5

Referenced by 266 Authors

5 Daniels, Harris B.
4 Roberts, David Peter
3 Dieulefait, Luis Victor
3 Fité, Francesc
3 González-Jiménez, Enrique
3 Kohlhase, Michael
3 Long, Ling
3 Najman, Filip
3 Rabe, Florian
3 Sijsling, Jeroen
3 Sutherland, Andrew V.
2 Akbary, Amir
2 Battistoni, Francesco
2 Bennett, Michael A.
2 Berčič, Katja
2 Billerey, Nicolas
2 Bruin, Peter
2 Cremona, John E.
2 Creutz, Brendan
2 Dawsey, Madeline Locus
2 Derickx, Maarten
2 Dummit, David S.
2 Freitas, Nuno
2 Gherga, Adela
2 Giangreco-Maidana, Alejandro José
2 Guitart, Xavier
2 Kazalicki, Matija
2 Lemos, Pedro
2 Linowitz, Benjamin
2 Marseglia, Stefano
2 Mascot, Nicolas
2 Masdeu, Marc
2 McCarthy, Dermot
2 Melistas, Mentzelos
2 Pacetti, Ariel
2 Pasten, Hector V.
2 Ramakrishnan, Balakrishnan
2 Sahu, Brundaban
2 Şengün, Mehmet Haluk
2 Soto, Eduardo
2 Stoll, Michael
2 Thorne, Jack A.
2 Top, Jaap
2 Verzobio, Matteo
2 Voight, John Michael
2 Wiesing, Tom
2 Wong, Peng-Jie
2 Zudilin, Wadim
1 Ahlgren, Scott D.
1 Altuğ, Salim Ali
1 Amir, Malik
1 Anni, Samuele
1 Arango-Piñeros, Santiago
1 Asif, Sualeh
1 Balakrishnan, Jennifer S.
1 Banwait, Barinder S.
1 Barquero-Sanchez, Adrian
1 Barrios, Alexander J.
1 Bartel, Alex
1 Bary-Soroker, Lior
1 Benjamin, Nathan
1 Berardini, Elena
1 Bergdall, John
1 Berger, Tobias
1 Bergeron, Nicolas
1 Bertin, Marie-Jose
1 Besser, Amnon
1 Bianchi, Francesca
1 Bisatt, Matthew
1 Brock, Bradley W.
1 Buzzard, Kevin
1 Calegari, Frank
1 Candelas, Philip
1 Chałupka, Karolina
1 Chamizo Lorente, Fernando
1 Chen, Imin
1 Chung, Hee-Joong
1 Collier, Scott
1 Cooper, Ian A.
1 Costa, Edgar
1 Cowan, Alex
1 Cully-Hugill, Michaela
1 de la Ossa, Xenia C.
1 Dehaye, Paul-Olivier
1 Deines-Schartz, Alyson
1 DeMark, David
1 Deo, Shaunak V.
1 Dogra, Netan
1 Dokchitser, Tim
1 Doris, Christopher
1 Dujella, Andrej
1 Duncan, John F. R.
1 Dunn, Alexander
1 Dutykh, Denys
1 Dwarshuis, Arjan
1 Earnest, Andrew G.
1 Elder, Gove Griffith
1 Elkies, Noam David
1 Elmi, Mohamed
1 Esparza-Lozano, Jose A.
...and 166 more Authors
all top 5

Referenced in 66 Serials

19 Mathematics of Computation
15 Research in Number Theory
10 Transactions of the American Mathematical Society
8 International Journal of Number Theory
7 The Ramanujan Journal
6 Acta Arithmetica
6 Journal de Théorie des Nombres de Bordeaux
5 Mathematische Annalen
4 Journal of Number Theory
4 Research in the Mathematical Sciences
3 Proceedings of the American Mathematical Society
3 Journal of High Energy Physics
2 Duke Mathematical Journal
2 Functiones et Approximatio. Commentarii Mathematici
2 Inventiones Mathematicae
2 Journal of the London Mathematical Society. Second Series
2 Mathematische Zeitschrift
2 Journal of the European Mathematical Society (JEMS)
2 Mediterranean Journal of Mathematics
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Annales Mathématiques du Québec
1 Communications in Algebra
1 Israel Journal of Mathematics
1 Journal of Mathematical Analysis and Applications
1 Nuclear Physics. B
1 Periodica Mathematica Hungarica
1 Advances in Mathematics
1 American Journal of Mathematics
1 Annales de l’Institut Fourier
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Archiv der Mathematik
1 Canadian Journal of Mathematics
1 Canadian Mathematical Bulletin
1 Colloquium Mathematicum
1 Glasgow Mathematical Journal
1 Journal of Algebra
1 Monatshefte für Mathematik
1 Nagoya Mathematical Journal
1 Proceedings of the London Mathematical Society. Third Series
1 Constructive Approximation
1 Revista Matemática Iberoamericana
1 Forum Mathematicum
1 Journal of the Ramanujan Mathematical Society
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Linear Algebra and its Applications
1 Indagationes Mathematicae. New Series
1 Experimental Mathematics
1 The New York Journal of Mathematics
1 Selecta Mathematica. New Series
1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 European Mathematical Society Newsletter
1 Transformation Groups
1 Mathematical Communications
1 Conformal Geometry and Dynamics
1 Moscow Mathematical Journal
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC
1 Mathematics in Computer Science
1 Journal of Physics A: Mathematical and Theoretical
1 Journal of Topology
1 Uniform Distribution Theory
1 Transactions of the London Mathematical Society
1 Discrete Analysis
1 Proceedings of the American Mathematical Society. Series B
1 Bollettino dell’Unione Matematica Italiana
1 SIAM Journal on Applied Algebra and Geometry

Referencing Publications by Year