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Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

The product of three translations along the directed sides of a triangle through twice the lengths of these sides is the identity map.

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

The rule which determines the orientation of the cross product u×v. The right-hand rule states that the orientation of the vectors' cross product is determined by placing u ...

The universal product code (UPC) is a 12-digit number and associated machine-readable bar code used to identify products being purchased in grocery stores. UPCs encode an ...

The Heath-Brown-Moroz constant is defined by C_(Heath-Brown-Moroz) = product_(p)(1-1/p)^7(1+(7p+1)/(p^2)) (1) = 0.00131764115... (2) (OEIS A118228), where the product is ...

The quadratic class number constant is a constant related to the average behavior of class numbers of real quadratic fields. It is given by Q = product_(p)[1-1/(p^2(p+1))] ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...