9 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009
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چکیده
We study the question of whether for each n there is an m �= n with λ(m) = λ(n), where λ is Carmichael’s function. We give a “near” proof of the fact that this is the case unconditionally, and a complete conditional proof under the Extended Riemann Hypothesis. –To Professor Carl Pomerance on his 65th birthday
منابع مشابه
INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 RECURSIVELY SELF - CONJUGATE PARTITIONS
A class of partitions that exhibit substantial symmetry, called recursively selfconjugate partitions, are defined and analyzed. They are found to have connections to non-squashing partitions and other combinatorial objects.
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We establish a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently. – Dedicated to Mel Nathanson on his 65th birthday
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The height of a polynomial with integer coefficients is the largest coefficient in absolute value. Many papers have been written on the subject of bounding heights of cyclotomic polynomials. One result, due to H. Maier, gives a best possible upper bound of nψ(n) for almost all n, where ψ(n) is any function that approaches infinity as n → ∞. We will discuss the related problem of bounding the ma...
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Let A be a set of n > n0(ε) positive real numbers, all at least 1 apart. We show that, if δa,b and δ� a,b are arbitrary real numbers satisfying |δa,b| < n 1−ε a , and |δ � a,b| < n1−ε b , we have |{(a + δa,b)(b + δ� a,b) : a, b ∈ A}| + |A + A| � n1+ε/9 log n . – Dedicated to Mel Nathanson and Carl Pomerance on the occasion of their 65th birthdays
متن کامل14 INTEGERS 9 Supplement ( 2009 ) MAIER MATRICES BEYOND
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تاریخ انتشار 2011