24 citations · 285 across the 74 of their papers we have counts for
6 papers · 1 filter
Asymptotically exact heuristics for prime divisors of a^k+b^k
Pieter Moree
Let N_{a,b}(x) count the number of primes p<=x with p dividing a^k+b^k for some k>=1. It is known that asymptotically N_{a,b}(x) grows like c(a,b)x/log x for some rational number c…
Convoluted convolved Fibonacci numbers
Pieter Moree
The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibon…
The formal series Witt transform
Pieter Moree
Given a formal power series f(z) we define, for any positive integer r, its rth Witt transform, W_f^{(r)}, by rW_f^{(r)}(z)=sum_{d|r}mu(d)f(z^d)^{r/d}, where mu is the Moebius func…
On a set-theoretic invariant
Dion Gijswijt, Pieter Moree
Let a_1,...,a_m be positive real numbers. Besser and Moree considered weighted numbers of -1,+1 solutions of the linear inequality |a_i-a_j| < e_ka_k < a_i+a_j, with e_k=-1 of 1 an…
Value distribution of Ramanujan sums and of cyclotomic polynomial coefficients
Pieter Moree, Huib Hommersom
The Ramanujan sum c_n(k) and a_n(k), the kth coefficient of the nth cyclotomic polynomial, are completely symmetric expressions in terms of primitive nth roots of unity. For fixed…
New Conjectures and Results for Small Cycles of the Discrete Logarithm
Joshua Holden, Pieter Moree
Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this que…