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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 19th 2014

added to modular form a brief paragraph with a minimum of information on modular forms As automorphic forms. Needs to be expanded.

• CommentRowNumber2.
• CommentAuthorGuest
• CommentTimeMar 1st 2021
I think the remark about them being sections of line bundles over the higher-genus Riemann moduli spaces is incorrect. Rather they should be sections of line bundles over modular curves.
1. Removed incorrect information about modular forms being sections of line bundles on Riemann moduli spaces. The Riemann moduli spaces for genus g > 1 are not even quotients of the upper half-plane (they are quotients of the genus g Teichmüller space, a higher-dimensional complex manifold) so none of the statements written even made sense. I believe what was intended was that they are sections of line bundles on modular curves, which are quotients of the upper half-plane.

Anonymous

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 2nd 2021

Thanks. It looks like I wrote this in rev 28, Sept. 2014.

• CommentRowNumber5.
• CommentTimeJul 2nd 2022

• CommentRowNumber6.
• CommentTimeJul 2nd 2022

Fixed reference to Diamond and Shurman, changed Wiles-Taylor to Taylor-Wiles.

• CommentRowNumber7.
• CommentTimeJul 2nd 2022

• CommentRowNumber8.
• CommentTimeJul 2nd 2022

Fixed reference to Deligne.

• CommentRowNumber9.
• CommentTimeJul 2nd 2022

• CommentRowNumber10.
• CommentTimeJul 2nd 2022

Added references related to the modularity theorem.

• CommentRowNumber11.
• CommentTimeJul 2nd 2022

Fixed references.

• CommentRowNumber12.
• CommentTimeJul 2nd 2022

Fixed references.

• CommentRowNumber13.
• CommentTimeJul 2nd 2022

• CommentRowNumber14.
• CommentTimeJul 2nd 2022

Added definition of modular forms as functions on elliptic curves with a choice of differential (following Calegari).

• CommentRowNumber15.
• CommentTimeJul 2nd 2022

Added section on action of Hecke operators on modular forms.

• CommentRowNumber16.
• CommentTimeJul 2nd 2022

Edited action of Hecke operators section.

• CommentRowNumber17.
• CommentTimeJul 2nd 2022

Added relation between Hecke eigenvalues and Fourier coefficients.

• CommentRowNumber18.
• CommentTimeJul 2nd 2022

Added some history behind Hecke operators.

• CommentRowNumber19.
• CommentTimeJul 2nd 2022

Added description of weight 2 cusp forms as differentials on the modular curve.

• CommentRowNumber20.
• CommentTimeJul 2nd 2022

Added section on L-functions of modular forms.

• CommentRowNumber21.
• CommentTimeJul 3rd 2022

Added description of L-function as a Mellin transform.

• CommentRowNumber22.
• CommentTimeJul 3rd 2022

Added description of L-function as a Mellin transform.

• CommentRowNumber23.
• CommentTimeJul 3rd 2022

• CommentRowNumber24.
• CommentTimeJul 3rd 2022

• CommentRowNumber25.
• CommentTimeJul 3rd 2022

Added references to original work of Hecke.

• CommentRowNumber26.
• CommentAuthorUrs
• CommentTimeJul 3rd 2022

• Erich Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I., Mathematische Annalen 114 (1937) 1–28 [doi:10.1007/BF01594160]

• Erich Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. II., Mathematische Annalen (in German), 114 (1937) 316–351 [doi:10.1007/BF01594180]

• CommentRowNumber27.
• CommentTimeJul 4th 2022

• CommentRowNumber28.
• CommentTimeJul 7th 2022

• CommentRowNumber29.
• CommentAuthorUrs
• CommentTimeAug 16th 2022