### 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 $$p \pmod q$$.

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

#### Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients (with Olivier Ramaré) Mathematika, 43, (1996), 73-107.

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