A Divisor Problem involving Prime Numbers

Asymptotic behaviour of some infinite products involving prime numbers

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 conto...

Asymptotic Behaviour of Some Infinite Products Involving Prime Numbers

Prime Slaughter: Playful Prime Numbers

Starting from the difficulty of creating playful representation of domain-specific abstract concepts, this study discusses the design of Prime Slaughter, a computer game aimed at facilitating individual sense-making of abstract mathematical concepts. Specifically the game proposes a transpositionmathematical concepts. Specifically the game proposes a transposition of primality and factorization...

On the Greatest Prime Divisor of Np

Let E be an elliptic curve defined over Q. For any prime p of good reduction, let Ep be the reduction of E mod p. Denote by Np the cardinality of Ep(Fp), where Fp is the finite field of p elements. Let P (Np) be the greatest prime divisor of Np. We prove that if E has CM then for all but o(x/ log x) of primes p ≤ x, P (Np) > p, where θ(p) is any function of p such that θ(p)→ 0 as p→∞. Moreover ...

Generalized divisor problem

In 1952 H.E. Richert by means of the theory of Exponents Pairs (developed by J.G. van der Korput and E. Phillips ) improved the above O-term ( see [8] or [4] pag. 221 ). In 1969 E. Krätzel studied the three-dimensional problem. Besides, M.Vogts (1981) and A. Ivić (1981) got some interesting results which generalize the work of P.G. Schmidt of 1968. In 1987 A.Ivić obtained Ω-results for ∫ T 1 ∆ ...