Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers

Details Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers

2009-03-13

arxiv.org/abs/0903.2514v2

Mathematics

Number Theory

Four references added in version 2

Scientific paper

A group of infinite products over low-order rational polynomials evaluated at the sequence of prime numbers is loosely called the Hardy-Littlewood constants. In this manuscript we look at them as factors embedded in a super-product over primes, semiprimes, 3-almost primes etc. Numerical tables are derived by transformation into series over k-almost prime zeta functions. Alternative product representations in a basis of k-almost prime products associated with Euler's formula for the Riemann zeta function are also pointed out.

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