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nLab > Latest Changes: Gauss sum

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1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTime5 days ago

    some minimum, for the moment just to state the evaluation formula for the plain quadratic Gauss sum

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTime5 days ago

    added (here) partial statement of the evaluation of the variant quadratic Gauss sum which has half the usual exponents (thanks to MO:a/489863 and MO:a/4232289)

    diff, v3, current

  3. correct English is halved not halfed. see e.g.

    https://www.merriam-webster.com/dictionary/halved

    https://en.wiktionary.org/wiki/halved#English

    Bee

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTime4 days ago

    Sure, thanks.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTime4 days ago

    have spelled out (here) the proof(s) for the evaluation of the quadratic Gauss sum with halved exponents for even numbers of summands.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTime4 days ago
    • (edited 4 days ago)

    have added the statement (here) of the evaluation, in terms of Jacobi symbols, of the quadratic Gauss sum with an extra integer factor in the exponent, for odd number of summands

    diff, v7, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTime2 days ago

    added pointer to:

    diff, v8, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTime2 days ago

    added (here) statement of the Landsberg-Schaar identity with references, which provides another evaluation of the quadratic Gauss sum with halved exponents (thanks to MO:a/489956)

    diff, v8, current

    • CommentRowNumber9.
    • CommentAuthorDmitri Pavlov
    • CommentTime2 days ago

    Added a Russian original (with a freely available full text that these days can be easily translated by a high-quality automatic translator even without the English version):

    • {#Ustinov22} Alexey Ustinov: A Short Proof of the Landsberg–Schaar Identity, Mathematical Notes 112 (2022) 488–490 [doi:10.1134/S0001434622090188]. Russian original: А. В. Устинов, Короткое доказательство тождества Ландсберга–Шаара, Математические заметки, 2022, том 112, выпуск 3, страницы 478–480, doi.

    diff, v9, current

1 to 9 of 9

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