Results 21 to 30 of about 31,249 (173)
Tau function and moduli of differentials [PDF]
, 2011 The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves.
Korotkin, Dmitry, Zograf, Peter
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Some new arithmetic functions [PDF]
Notes on Number Theory and Discrete MathematicsWe introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
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Recursive Determination of the Sum-of-Divisors Function [PDF]
Proceedings of the American Mathematical Society, 1979 A recursive scheme for determination of the sum-of-divisors function is presented. As all of the formulas involve triangular numbers, the scheme is therefore compared for efficiency with another known recursive triangular-number formula for this function.
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A Generalization of the Sum of Divisors Function
, 2022 A generalization of the sum of divisors function involves a recursive definition. This leads to variants of superabundant numbers, colossally abundant numbers, and Gronwall's theorem (relevant to the Riemann hypothesis).
Darrell Cox +2 more
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Extremal orders of some functions connected to regular integers modulo n
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of , , , , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for and ,
Brăduţ Apostol
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Nonaliquots and Robbins Numbers [PDF]
, 2005 http://www.math.missouri.edu/~bbanks/papers/index.htmlLet '(•) and _(•) denote the Euler function and the sum of divisors function, respectively. In this paper, we give a lower bound for the number of m ≤ x for which the equation m = _(n)−n has no ...
Banks, William David, 1964- +1 more
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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On the average value of the least common multiple of k positive integers [PDF]
, 2016 We deduce an asymptotic formula with error term for the sum ∑n1,…,nk≤xf([n1,…,nk]), where [n1,…,nk] stands for the least common multiple of the positive integers n1,…,nk (k≥2) and f belongs to a large class of multiplicative arithmetic functions ...
Alladi +24 more
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Arithmatical consequences of two identities of B. Gordon
International Journal of Mathematics and Mathematical Sciences, 1979 From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function ...
John A. Ewell
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Variations on a theorem of Davenport concerning abundant numbers [PDF]
, 2013 Let \sigma(n) = \sum_{d \mid n}d be the usual sum-of-divisors function. In 1933, Davenport showed that that n/\sigma(n) possesses a continuous distribution function. In other words, the limit D(u):= \lim_{x\to\infty} \frac{1}{x}\sum_{n \leq x,~n/\sigma(n)
Jennings, Emily +2 more
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