Titlebook: Analytic and Elementary Number Theory; A Tribute to Mathema K. Alladi,P. D. T. A. Elliott,G. Tenebaum Book 1998 Springer-Verlag US 1998 Dis

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https://doi.org/10.1007/978-3-0348-8645-1number of unrestricted partitions of ., .(.), the number of partitions of . into distinct parts and the Rogers-Ramanujan partitions of . (of both types). The weights derived here are given either in terms of congruence conditions satisfied by the parts or in terms of chains of gaps between the parts

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Discrete Structural Optimizationthe number of totients ≥., .(.), the number of solutions of .(.) . (the “multiplicity” of .), and ..(.), the number of . ≤ . with .(.) .. The first of the main results of the paper is a determination of the true order of . (.). It is also shown that for each . ≥ 1, if there is a totient with multipl

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Discrete Structural Optimizationeasing size), is ordered lexicographically. This concept easily yields to a new type of multiplicative structure for the exceptional set in the Maier-Tenenbaum theorem on the propinquity of divisors, which settled a well-known conjecture of Erdős. We provide asymptotic formulae for the number of lex

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Husserl and the Reform of Logicentations of an integer as a sum of five squares. (Here . (.) denotes the sum of the divisors of . if . is a positive integer and . (0) = -1/24.).Several related identities are derived and discussed..Two devices are used in the proofs. The first device establishes the equality of two expressions, ne

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Developments in Mathematicshttp://image.papertrans.cn/a/image/156559.jpg

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https://doi.org/10.1007/978-1-4757-4507-8Distribution; Maximum; Modular form; Prime; Prime number; Riemann zeta function; number theory; combinatori

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978-1-4419-5058-1Springer-Verlag US 1998

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