S. Böcherer, R. Schulze-Pillot

Corrections (February 2003) to our article “On the central critical value of the triple product L-function” (appeared in: Number Theory 1993-94, 1-46. Cambridge University Press, 1996)

• p.5: l.8 f.a.: read (L_{α}^{(b)}f) rather than (L_{α}^{(b)})

• p.5: l.9 f.b. read ∂_{12}X_{2} rather than ∂_{12}X_{1}

• p.7: l.12 f.b.: read ”(1.9)” rather than ”(1.10)”

• p.7: Skip the sentences ”It is easy...” (l.8 f.b.) until ”...polynomial in ∂_{12}, ∂_{13}, ∂_{23} (l.5 f.b.)

• p.7: l.4.f.b.: read a′ rather than a

• p.7: l.3 f.b.:Formula (1.11) should read

\frac{2^{b}2^{a′}(2i)^{3a′}}{(α + a′)^{[b]}b!} (∂_{12}∂_{13}∂_{23})^{a′} (∂_{12}X_{2} + ∂_{13}X_{3})^{b}

• p.9: l.11 f.a.: read a′ rather than a

• p.12 l.8 f.b.: the formula should be

A(s, b) = (−1)^{b} · \frac{2^{−a}(2s − 2)^{[a]}(s)^{[a′]}(2s + a − 2)^{[b]}}{b!(s + a′ − 1)^{[b]}}

• p.13: in formula (2.11)

(g < Z >^{∗}) rather than × < g < Z >^{∗}>
det^{k+a} rather than det^{k+a}

• p.17: l.7 f.b.: read h′ rather than h

• p.18: delete factor 2 in formula (2.28)

• p.32 in formula (4.1) read L_{p}(f, ϕ, ψ, s + 3a′ + 2r + b − 2)

• p.33 Formula (4.3) is correct only under the additional assumption r = 2

• p.33 In (4.3) read ζ rather than zeta

• p.33 In the functional equation (4.4) the exponent of N should be −4(s − \frac{k_{1}+k_{2}+k_{3}}{2} + 1); the exponent of gcd(N_{f}, N_{ϕ}, N_{ψ}) should be −(s − \frac{k_{1}+k_{2}+k_{3}}{2} + 1)

• p.34: l.10: read allows for p | N rather than allows for p ∤ N

• p.35: l.5.f.a.: read (2.1) rather than (2.2)

• p.37: l.9 f.b. read i^{3a′}π^{3a′+b} rather than π^{3a+2b}

• p.37: l.7 f.b: read (i^{3a′}π^{3a′+b})^{−1} rather than π^{−3a−2b}

• p.38: in formula 5.4: read i^{3a′}π^{3a′+b} rather than π^{3a+2b} • p.42:

In Lemma 5.5 and in line 19 read

(∑_{i=1}^{h} \frac{T_{0}(φ_{f}(y_{i}) ⊗ φ_{ϕ}(y_{i}) ⊗ φ_{ψ}(y_{i}))}{e_{i}})

• p.44: The first line of formula (5.9) should read

(−1)^{ω(N)+ω(M_{1},M_{2})}2^{5+3b+8a′−ω(gcd(N_{f} ,N_{ϕ},N_{ψ})}π^{5+6a′+2b}

×N^{2}(M_{1}M_{2})^{−3}M_{3}^{−6} \frac{1}{\binom{b}{ν_{2}}} \frac{b!(a′ + 1)^{[b]}}{2^{[a]}2^{[a′]}(a + 2)^{[b]}}

×\frac{(a′ + b + 1)Γ(2a′ + b + 2)}{Γ(3a′ + b + 2)Γ(a′ + ν_{2} + 1)Γ(a′ + ν_{3} + 1)}

• p.45: l.8.f.a.: Nagoya Math.J.147(1997), 71-106

• p.45 l.3 f.b.: Comm.Math.Univ.S.Pauli 48(1999), 103-118