Linear programming over exponent pairs

Lelechenko, Andrew V.

doi:10.2478/ausi-2014-0014

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Moments Of ζ1

Multiexponential Divisor Functions1

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2013

2024

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Cited by 3 publications

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“…To apply Theorem 1 efficiently, we need a method to evaluate infimums of form ( 5) and ( 6) over exponent pairs. We have developed such framework, whose initial version has been described in [9]. Since then the framework has been developed further and released as a exp-pairs…”

Section: Moments Of ζmentioning

confidence: 99%

Dirichlet divisor problem on Gaussian integers

Lelechenko¹

2018

Preprint

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Section: Moments Of ζmentioning

confidence: 99%

Dirichlet divisor problem on Gaussian integers

Lelechenko¹

2018

Preprint

Self Cite

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“…5.11, Th. 5.12], selecting appropriate exponent pair using the method described in [12]; see Table 1. 1.…”

Section: Multiexponential Divisor Functionsmentioning

confidence: 99%

Exponential divisor functions

Lelechenko¹

2013

Preprint

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Consider the operator E on arithmetic functions such that Ef is the multiplicative arithmetic function defined by (Ef )(p a ) = f (a) for every prime power p a . We investigate the behaviour of E m τ k , where τ k is a kdimensional divisor function and E m stands for the m-fold iterate of E. We estimate the error terms of n x E m τ k (n) for various combinations of m and k. We also study properties of E m f for arbitrary f and sufficiently large m.Our study provides a unified approach to functions with exponential divisors. We improve special cases of the Dirichlet asymmetric divisor problem and several results on the exponential divisor and totient functions.

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Toward optimal exponent pairs

Trudgian,

Yang

2024

Math. Comp.

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We quantify the set of known exponent pairs ( k , ℓ ) (k, \ell ) and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Riemann zeta-function ζ ( s ) \zeta (s) in the critical strip, estimates of the moments of ζ ( 1 / 2 + i t ) \zeta (1/2 + it) and the generalised Dirichlet divisor problem.

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Linear programming over exponent pairs

Cited by 3 publications

References 7 publications

Dirichlet divisor problem on Gaussian integers

Dirichlet divisor problem on Gaussian integers

Exponential divisor functions

Toward optimal exponent pairs

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