Asymptotic behaviour of some infinite products involving prime numbers
نویسنده
چکیده
The asymptotic behaviour of some entire functions defined via infinite products is investigated as the parameter z tends to infinity in the sector | arg z| < π. These functions arise in the distributions of the number of prime factors of integers and of the number of irreducible factors of monic polynomials over a finite field. Our approach is based on the Mellin transform with a suitable contour of Hankel type (the integrand encountered having either logarithmic or algebraic singularity rather than poles). The methods are also applicable to other classes of entire functions.
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