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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 (p1)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.

Article

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. .

Article
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}

Article

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.

Article