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On the Density of the Odd Values of the Partition Function
Başlık:
On the Density of the Odd Values of the Partition Function
Yazar:
Judge, Samuel D., author.
ISBN:
9780355979442
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (87 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Fabrizio Zanello Committee members: John A. Jaszazak; William J. Keith; Melissa S. Keranen.
Özet:
The purpose of this dissertation is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function p(n) is equidistributed modulo 2. We provide a doubly-indexed, infinite family of conjectural identities in the ring of series Z2[[ q]], which relate p(n) with suitable t-multipartition functions, and show how to, in principle, prove each such identity. We will exhibit explicit proofs for 32 of our identities. However, the conjecture remains open in full generality.
A striking consequence of these conjectural identities is that, under suitable existence conditions, for any t coprime to 3, if the t-multipartition function is odd with positive density, then p(n) is also odd with positive density. Additionally if any t-multipartition function is odd with positive density, then either p(n) or the 3-multipartition function (or both) are odd with positive density. All of these facts appear virtually impossible to show unconditionally today.
Our arguments employ a combination of algebraic and analytic methods, including certain technical tools recently developed by Radu in his study of the parity of the Fourier coefficients of modular forms.
Notlar:
School code: 0129
Konu Başlığı:
Tüzel Kişi Ek Girişi:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(679871.1) | 679871-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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