Cohen-Kaplansky domains and the Goldbach conjecture
نویسندگان
چکیده
منابع مشابه
The Goldbach Conjecture*
In the 20th century, many great mathematicians were attracted by this conjecture. In 1900, D. Hilbert gave a famous speech in an international mathematical conference, in which he proposed 23 problems to mathematicians. The Goldbach conjecture is a part of his 8th problem and the other part is the Riemann hypothesis. G. H. Hardy said that the Goldbach conjecture is one of the most difficult pro...
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PROOF. Let A be a C*-algebra, ' a derivation of A. It is enough to show that the derivation is continuous on the self-adjoint portion As of A. Therefore if it is not continuous, by the closed graph theorem there is a sequence \xn\ (xn 4= 0) in As such that xn -»0 and xn -> a + ίέ(φθ), where a and b are self-adjoint. First, suppose that a =f= 0 and there exists a positive number λ(> 0) in the sp...
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A conjecture was related to this author in correspondence, some years ago, with Irving Kaplansky, which according to Professor Kaplansky, was inspired by the proof of [4, Theorem 6.5.9, p. 348]. It asserts that if p is a prime with representation p = a2 + (2b)2, then the equation x2 − py2 = a is solvable in integers x, y. In [5], we proved this conjecture along with several others by him. Subse...
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The purpose of this paper is to show how adelic ideas might be used to make progress on the Goldbach Conjecture. In particular, we present a new Schwartz function which is able to keep track of the number of prime factors of an integer. We then use this, along with the Ono/Igusa adelic methods for Diophantine equations, to present an infinite sum whose evaluation would prove or disprove the ver...
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It is proved that for a given integer N and for all but (log N)B prime numbers k ≤ N5/48−ε the following is true: For any positive integers bi, i ∈ {1, 2, 3}, (bi, k) = 1 that satisfy N ≡ b1 + b2 + b3 (mod k), N can be written as N = p1+p2+p3, where the pi, i ∈ {1, 2, 3} are prime numbers that satisfy pi ≡ bi (mod k).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11086-4