Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis

ERRATA

PAGE/LINE

5/−12  for ‘−/π’ read ‘−1/π’
71/−18  replace ‘N_{b}(N; b)’ by ‘J_{b}(N; b)’
71/−17  replace ‘k < j ≤ b’ by ‘b < j ≤ k’
71/−16  replace ‘N_{k}(N; b)’ by ‘J_{k}(N; b)’ twice, and

‘N_{b}(N; b)’ by ‘J_{b}(N; b)’

83/−11  delete the ‘¡’
88/−6  replace ‘,’ by ‘.’
90/−17  replace ‘r^{−1/3}’ by ‘r^{1/3}’
91/1  replace ‘δ/3’ by ‘δ/2’
91/2  replace ‘re(α)’ by ‘z’
91/4  replace ‘∑_{n=0}^{Ck}’ by ‘∑_{n=k}^{Ck}’
91/−6  replace ‘Q(1) = 1’ by ‘Q(1) = 0’
92/−13  replace ‘Δ_{d}’ by ‘Δ_{d+1}’
92/−12  ditto
92/−1  between ‘max’ and ‘≫’ insert ‘|s_{ν}|’
93/−6  replace ‘s_{n}’ by ‘s_{ν}’
94/4  the sum should be surrounded by

absolute value signs

95/11  replace ‘(\frac{L}{4})^{N}’ by ‘(\frac{L}{4})^{d}’
95/−13  replace ‘c_{k}| ≤ C’ by ‘|c_{k}| ≤ C’
115/9  replace ‘\frac{d}{dx}’ by ‘\frac{d}{ds}’
115/13  wrong font: ‘N’ should be ‘N’
116/4  replace ‘= ∫_{𝒞} 1 ds = |𝒞|’ by ‘= 2 ∫_{𝒞} 1 ds = 2|𝒞|’
160/10  replace ‘Backer’ by ‘Baker’
164/12  replace ‘0 < δ ≤ 1/2’ by ‘1/ log q ≤ δ ≤ 1/2’

[Thanks to Ronnie Burthe for spotting this error, and to Carl Pomerance for reporting it.]

164/−11, −10  Delete the first two sentences in the

proof of Theorem 1.

196/−5  replace ‘a_{k}x^{k}’ by ‘a_{j}x^{j}’
197/−14  The right hand side should be

multiplied by ‘H/N’

197/−12  The right hand side should be divided by ‘N’
197/−7  between ‘N^{B}’ and ‘.’ insert

‘where s_{ν} = ∑_{n=1}^{N} z_{n}^{ν}’

202/2  The problem was solved by Heath-Brown.
202/14  In the sum, replace ‘f(a)’ by ‘f(b)’