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nLab > Latest Changes: modular form

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  1.  
    • 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.

  3. 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

    diff, v31, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 2nd 2021

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

    • CommentRowNumber5.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added relation to Galois representations.

    diff, v34, current

    • CommentRowNumber6.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

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

    diff, v34, current

    • CommentRowNumber7.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added reference to Deligne.

    diff, v34, current

    • CommentRowNumber8.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Fixed reference to Deligne.

    diff, v34, current

    • CommentRowNumber9.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added Deligne-Serre reference.

    diff, v34, current

    • CommentRowNumber10.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added references related to the modularity theorem.

    diff, v34, current

    • CommentRowNumber11.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Fixed references.

    diff, v34, current

    • CommentRowNumber12.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Fixed references.

    diff, v34, current

    • CommentRowNumber13.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added definition as function on lattices, following Calegari (added as reference).

    diff, v35, current

    • CommentRowNumber14.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

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

    diff, v35, current

    • CommentRowNumber15.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added section on action of Hecke operators on modular forms.

    diff, v35, current

    • CommentRowNumber16.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Edited action of Hecke operators section.

    diff, v35, current

    • CommentRowNumber17.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added relation between Hecke eigenvalues and Fourier coefficients.

    diff, v36, current

    • CommentRowNumber18.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added some history behind Hecke operators.

    diff, v36, current

    • CommentRowNumber19.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

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

    diff, v37, current

    • CommentRowNumber20.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added section on L-functions of modular forms.

    diff, v38, current

    • CommentRowNumber21.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 3rd 2022

    Added description of L-function as a Mellin transform.

    diff, v40, current

    • CommentRowNumber22.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 3rd 2022

    Added description of L-function as a Mellin transform.

    diff, v40, current

    • CommentRowNumber23.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 3rd 2022

    Added definition of cusp form.

    diff, v40, current

    • CommentRowNumber24.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 3rd 2022

    Linked to cusp form.

    diff, v41, current

    • CommentRowNumber25.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 3rd 2022

    Added references to original work of Hecke.

    diff, v42, current

    • CommentRowNumber26.
    • CommentAuthorUrs
    • CommentTimeJul 3rd 2022

    I have also added the DOI-links:

    • 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]

    diff, v43, current

    • CommentRowNumber27.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 4th 2022

    Added link to Hecke correspondence.

    diff, v44, current

    • CommentRowNumber28.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 7th 2022

    Added description as Mellin transform, link to Langlands program.

    diff, v45, current

    • CommentRowNumber29.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2022

    added pointer to today’s:

    diff, v46, current

    • CommentRowNumber30.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 23rd 2022

    Added link to p-adic modular form.

    diff, v47, current

    • CommentRowNumber31.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2023

    added pointer to:

    diff, v48, current

  32. Fixed typo.

    Joseph Martin

    diff, v49, current

1 to 32 of 32

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