Equal sums in random sets and the concentration of divisors

Equal sums in random sets and the concentration of divisors

We study the extent to which divisors of a typical integer n are concentrated. In particular, defining Δ(𝑛):=max𝑡#{𝑑|𝑛,log𝑑∈[𝑡,𝑡+1]}, we show that Δ(𝑛)⩾(loglog𝑛)0.35332277… for almost all n, a bound we believe to be sharp. This disproves a conjecture of Maier and Tenenbaum. We also prove analogs for...

书目详细资料
Main Authors:	Ford, K, Green, B, Koukoulopoulos, D
格式:	Journal article
语言:	English
出版:	Springer 2023

相似书籍

On a Sum Involving the Sum-of-Divisors Function
由: Feng Zhao, et al.
出版: (2021-01-01)

On the sum of positive divisors functions
由: Erban, R, et al.
出版: (2021)

On the divisor sums in arithmetical progressions
由: Eugenijus Stankus
出版: (1998-12-01)

A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
由: M. Haris Mateen, et al.
出版: (2022-01-01)

Moments of zeta and correlations of divisor-sums: V
由: Conrey, B, et al.
出版: (2018)

Sums of divisor functions in Fq[t] and matrix integrals
由: Keating, J, et al.
出版: (2017)

On the average value of divisor sums in arithmetic progressions
由: Heath-Brown, D, et al.
出版: (2005)

Retracted: A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
由: Journal of Chemistry
出版: (2023-01-01)

Sum of the triple divisor function of mixed powers
由: Li Zhou, et al.
出版: (2022-05-01)

A survey of the alternating sum-of-divisors function
由: Tóth László
出版: (2013-02-01)

DISTRIBUTION OF VALUES OF THE SUM OF UNITARY DIVISORS IN RESIDUE CLASSES
由: B. M. Shirokov, et al.
出版: (2016-05-01)

Average Size of Ramanujan Sum Associated with Divisor Function
由: Xin Li, et al.
出版: (2025-02-01)

Moment estimates for the exponential sum with higher divisor functions
由: Pandey, Mayank
出版: (2022-05-01)

The multinomial convolution sum of a generalized divisor function
由: Park Ho
出版: (2022-06-01)

Averages of ratios of the Riemann zeta-function and correlations of divisor sums
由: Conrey, B, et al.
出版: (2017)

The structure of multiplicative functions with small partial sums
由: Dimitris Koukoulopoulos, et al.
出版: (2020-05-01)

Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions
由: Daeyeoul Kim, et al.
出版: (2014-01-01)

Exponential sums involving the divisor function over arithmetic progressions
由: Rui Zhang, et al.
出版: (2023-03-01)

Iterating the Sum of Möbius Divisor Function and Euler Totient Function
由: Daeyeoul Kim, et al.
出版: (2019-11-01)

On certain upper bounds for the sum of divisors function σ(n)
由: Sándor József, et al.
出版: (2015-12-01)

The sixth moment of the Riemann zeta function and ternary additive divisor sums
由: Nathan Ng
出版: (2021-07-01)

Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices
由: Daeyeoul Kim, et al.
出版: (2014-01-01)

Sums of the higher divisor function of diagonal homogeneous forms in short intervals
由: Huimin Wang, et al.
出版: (2023-07-01)

A note on representations of the finite Heisenberggroup and sums of greatest common divisors
由: Johannes Grassberger, et al.
出版: (2001-12-01)

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
由: Jin Seokho, et al.
出版: (2024-11-01)

On some geometric properties of sequence spaces of generalized arithmetic divisor sum function
由: Mohammad Mursaleen, et al.
出版: (2024-09-01)

A note on representations of the finite Heisenberg group and sums of greatest common divisors
由: Johannes Grassberger, et al.
出版: (2001-01-01)

Arithmetic convolution sums derived from eta quotients related to divisors of 6
由: Ikikardes Nazli Yildiz, et al.
出版: (2022-04-01)

Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality
由: Wenruo Lyu, et al.
出版: (2023-07-01)

A logarithmic estimate for harmonic sums and the digamma function, with an application to the Dirichlet divisor problem
由: G. J. O. Jameson
出版: (2019-05-01)

Rational Divisors in Rational Divisor Classes.
由: Bruin, N, et al.
出版: (2004)

Rational divisors in rational divisor classes
由: Bruin, N, et al.
出版: (2004)

Equal sums of three powers
由: Browning, T, et al.
出版: (2004)

Equal Sums of three powers
由: Browning, T, et al.
出版: (2004)

Divisor problem in special sets of Gaussian integers
由: O.V. Savastru
出版: (2016-12-01)

Simultaneous equal sums of three powers
由: Heath-Brown, D, et al.
出版: (2007)

Classification of Zero Divisor Graphs of a Commutative Ring With Degree Equal 7 and 8
由: Nazar Shuker, et al.
出版: (2013-07-01)

Eulerian and pancyclic zero-divisor graphs of ordered sets
由: Nilesh Khandekar, et al.
出版: (2024-09-01)

Bipartite divisor graph for the set of irreducible character degrees
由: Roghayeh Hafezieh
出版: (2017-12-01)

Brief survey on divisor graphs and divisor function graphs
由: Vignesh Ravi, et al.
出版: (2023-05-01)