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Brewer sum

Yilda matematika, Pivo summalari cheklangan belgilar yig'indisi Brewer tomonidan kiritilgan (1961, 1966) bog'liq bo'lgan Jakobstalning summasi.

Ta'rif

Brewer summasi tomonidan berilgan

{ displaystyle Lambda _ {n} (a) = sum _ {x { bmod {p}}} { binom {D_ {n + 1} (x, a)} {p}}}

qayerda D._n bo'ladi Dikson polinomi (yoki "Brewer polynomial") tomonidan berilgan

{ displaystyle D_ {0} (x, a) = 2, quad D_ {1} (x, a) = x, quad D_ {n + 1} (x, a) = xD_ {n} (x, a) -aD_ {n-1} (x, a)}

va () bu Legendre belgisi.

Brewer summasi qachon nolga teng n bu koprime ga q²−1.

Adabiyotlar

Brewer, B. W. (1961), "Muayyan belgilar yig'indisi to'g'risida", Amerika Matematik Jamiyatining operatsiyalari, 99 (2): 241–245, doi:10.2307/1993392, ISSN 0002-9947, JSTOR 1993392, JANOB 0120202, Zbl 0103.03205
Brewer, B. W. (1966), "u² + 5v² shaklidagi asoslar to'g'risida", Amerika matematik jamiyati materiallari, 17 (2): 502–509, doi:10.2307/2035200, ISSN 0002-9939, JSTOR 2035200, JANOB 0188171, Zbl 0147.29801
Berndt, Bryus S.; Evans, Ronald J. (1979), "Gauss, Eyzenshteyn, Jakobi, Jeykobstal va Brewerning summalari", Illinoys matematikasi jurnali, 23 (3): 374–437, ISSN 0019-2082, JANOB 0537798, Zbl 0393.12029
Lidl, Rudolf; Niderreyter, Xarald (1997), Cheklangan maydonlar, Matematika entsiklopediyasi va uning qo'llanilishi, 20 (2-nashr), Kembrij universiteti matbuoti, ISBN 0-521-39231-4, Zbl 0866.11069

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