Errata: Vinogradov's integral and bounds for the Riemann zeta function, Proc. London Math. Soc. (3) 85 (2002), 565-633.

All corrections have been made to the PDF file on my web page. Page numbers refer to the published version.

1. page 578. After the definition of q(t), delete the next two sentences. The reason that c' is a permutation of c is that the two polynomials ∏ (t-ci) and ∏ (t-c'i) are identical over the field of p elements.

2. page 582, line -3. Φ' should not have the dash above it.

3. page 600. First sentence of section 5. Replace λ ≥ 84 with λ ≥ 87.

4. page 605, (5.17). the exponent of P needs to be 2s - t(h+g)/2 + E2 .

5. page 612, line -3. Replace mk with Mk in the inequality.