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Various Old and New Results in Classical Arithmetic by Special Functions
Başlık:
Various Old and New Results in Classical Arithmetic by Special Functions
Yazar:
Henry, Michael, author.
ISBN:
9780438092952
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (58 pages)
Genel Not:
Source: Masters Abstracts International, Volume: 57-06M(E).
Advisors: Gang Yu Committee members: Oma De la Cruz Cabrera; Ulrike Vorhauer.
Özet:
Beginning with the essentials from the theory of simple continued fractions, we review some early results in Diophantine approximation. We proceed to prove that Liouville's number L is transcendental; in addition we discuss the transcendence measure of e, known as Davis' theorem, which also gives us e is a transcendental number by Roth's theorem. Having reviewed these results we generalize a result of Landau, giving rise to what we will call Landau sums. These sums generate a countable spectrum of irrational numbers that are computable in quadratic time due to their representation as theta functions; it is still open as to whether these numbers are transcendental. Altering the Landau sums we also get another class of sums that we call lateral Landau sums. These sums also give a spectrum of numbers that we speculate are irrational. These results sit nicely within the intersection of classical analysis and classical number theory. We say a few words about this relationship and end with some conjectures.
Notlar:
School code: 0101
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(696287.1) | 696287-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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