<abstract xmlns="http://www.w3.org/1999/xhtml">Investigation has been made regarding the properties of the ℿp<italic>≤</italic>n (1 <italic>±</italic> 1/ps) products over the prime numbers, where we fix the s <italic>∈</italic> ℝ exponent, and let the n <italic>≥</italic> 2 natural bound grow toward positive infinity. The nature of these products for the s <italic>≥</italic> 1 case is known. We get approximations for the case when s <italic>∈</italic> [1/2, 1), furthermore different observations for the case when s&lt;1/2.</abstract>

Investigation has been made regarding the properties of the ℿp≤n (1 ± 1/ps) products over the prime numbers, where we fix the s ∈ ℝ exponent, and let the n ≥ 2 natural bound grow toward positive infinity. The nature of these products for the s ≥ 1 case is known. We get approximations for the case when s ∈ [1/2, 1), furthermore different observations for the case when s<1/2.

On Euler products with smaller than one exponents

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On Euler products with smaller than one exponents"}

Investigation has been made regarding the properties of the ℿp≤n (1 ± 1/ps) products over the prime numbers, where we fix the s ∈ ℝ exponent, and let the n ≥ 2...

On Euler products with smaller than one exponents

Published Online: Jul 16, 2020

Page range: 193 - 211

Received: Aug 15, 2019

DOI: https://doi.org/10.2478/ausm-2020-0013

Keywords
Euler product, Mertens’ theorem, Riemann zeta function, Abel summation, Riemann hypothesis, prime number theorem, logarithmic integral

© 2020 Gábor Román, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On Euler products with smaller than one exponents

Published Online: Jul 16, 2020

Page range: 193 - 211

Received: Aug 15, 2019

DOI: https://doi.org/10.2478/ausm-2020-0013

KeywordsEuler product, Mertens’ theorem, Riemann zeta function, Abel summation, Riemann hypothesis, prime number theorem, logarithmic integral

© 2020 Gábor Román, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Euler product, Mertens’ theorem, Riemann zeta function, Abel summation, Riemann hypothesis, prime number theorem, logarithmic integral