Andrew Granville's Home Page

1996 Publications

Values of Bernoulli polynomials (with Zhi-Wei Sun)
Pacific Journal of Mathematics, 172 (1996), 117-137.

We show that the value of the \( (p-1)\)st Bernoulli polynomial at \( a/q\) can be given, mod \( p\), in terms of a certain linear recurrence of order \( [q/2]\), which depends only on \( a,q\) and \( p \pmod q\).


Defect zero \( p\)-blocks for finite simple groups (with Ken Ono)
Transactions of the American Mathematical Society, 348 (1996), 331-334.

We classify those finite simple groups whose Brauer graph has a \( p\)-block with defect 0. .

We prove Erdos's conjecture that \( \binom {2n}n\) is not squarefree for all \( n>4\), by obtaining explicit upper bounds on exponential sums of the form \( \sum_n \Lambda(n)e(x/n) \) for \( n\sim N\ll x^{3/5}\)


On the number of co-prime-free sets (with Neil Calkin)
Number Theory: New York Seminar 1991-1995, (D. Chudnovsky, G. Chudnovsky and M. Nathanson, eds) Springer-Verlag, 1996, 9-18.

We investigate the number of subsets of the integers up to \( x\) that have certain given arithmetic properties.