Pascal Sebah

We study the asymptotics of the average number of squares (or quadratic residues) in Z_n and Z_n^*. Similar analyses are performed for cubes, square roots of 0 and 1, and cube roots of 0 and 1.

Consider the product of (1-p^(-s))^(-4) over all primes p=1 mod 5. We evaluate its residue at s=1 and compare with the corresponding Mertens constant of Languasco & Zaccagnini. We also count primitive quintic Dirichlet characters mod n and…

Let f(n) denote the number of odd entries in the nth row of Pascal's binomial triangle. We study "average dispersion" and "typical dispersion" of f(n) -- the latter involves computing a generalized Lyapunov exponent -- and then turn to…

The nth row of Pascal's trinomial triangle gives coefficients of (1+x+x^2)^n. Let g(n) denote the number of such coefficients that are odd. We review Moshe's algorithm for evaluating asymptotics of g(n) -- this involves computing the…