منابع مشابه
The least k-th power non-residue
Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least k-th power non-residue modp is at most 3.9p log p unless k = 2 and p ≡ 3 (mod 4), in which case the bound is 4.7p log p. With a combinatorial idea and a little help from computing power, we improve the upper bounds to 0.9p log p and 1.1p log p, respectively.
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I review the k-factorization method to combine the high-energy behaviour in QCD with the renormalization group. Resummation formulas for coefficient functions and anomalous dimensions are derived, and their applications to small-x scaling violations in structure functions are briefly discussed. ∗) Talk delivered at the VIth Blois Workshop “Frontiers in Strong Interactions”, June 20-24, 1995. +)...
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We present an efficient randomized algorithm for the approximate k-th selection problem. It works in-place and it is fast and easy to implement. The running time is linear in the length of the input. For a large input set the algorithm returns, with high probability, an element which is very close to the exact k-th element. The quality of the approximation is analyzed theoretically and experime...
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This paper continues the study of Alexandrov–Fenchel inequalities for quermassintegrals for k-convex domains. It focuses on the application to the Michael–Simon type inequalities for k-curvature operators. The proof uses optimal transport maps as a tool to relate curvature quantities defined on the boundary of a domain. Mathematics Subject Classification (2010) Primary 35J96 · Secondary 52B60
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The conductor of a rational integer is the product of the primes which divide it. The lower k-th root is the largest k-th power divisor, and the upper k-th root is the smallest k-th power multiple. This paper examines the relationships between these arithmetic functions and their Dirichlet series. It is shown that the conductor is the limit of the upper k-th roots in two different ways as k ten...
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ژورنال
عنوان ژورنال: Journal of Applied Crystallography
سال: 1974
ISSN: 0021-8898
DOI: 10.1107/s0021889874010181