On Euler products with smaller than one exponents

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.

Keywords

• euler product
• mertens’ theorem
• riemann zeta function
• abel summation
• riemann hypothesis
• prime number theorem
• logarithmic integral
• 11m99