Prof. Siegel has been kind enough to point out to me the reason for the difference between my formula (6.23), p. 544, and the corresponding formula on p. 166 of Hecke's paper, my formula containing a constant C11 which is absent from Hecke's formula. Hecka, in deducing his formula on p. 163, line 6 up, from the first formula on the same page (when k = 1) by deforming the path of integration, has overlooked the residue arising from the pole s = 0. The investigation of the simplest form and properties of C11 would be interesting. I am also indebted to Prof. Siegel for the majority of the following corrections: P. 505, formula 2. 3. For μ c (mod a) read μ ≡ c (mod a). P. 534, l. 7 up. For 1, ε, ε2, ε3, … read ±1, ±ε, ±ε2, ±ε3, …. P. 536, l. 11. In the exponent, for λ′e−tc. read λ′e−tc′. P. 537, l. 5 For a read a. P. 537, l. 10. For a = β = 1 read a = β = 0. P. 538, l. 11. For − i τ 2 π read − i τ 2 π Δ . P. 538, l. 2 up. For η + τ sgn η read η + τ sgn λ. P. 540, formula (6.10). For −2πiτ log ε read −2iτ log ε. P. 541, foot. For | Δ | read | Δ | D . P. 542, l. 8. For S(λρ) ≡ S(σ′ρ) (mod aQD) read S(λρ)≡S(σ′ρ) (mod AQD). P. 544, l. 4. For cτ read iτ. P. 544, l. 5. For D(iη; ρ′, a′) read D(iη′, σ′, a′). P. 548, 1. 4. In the exponent, for −τ(μ2t2 + μ′2) read −2τ|μμ′|. P. 551, l. 1. For P read η. P. 551, l. 2. For ξ, η read ξ, P. P. 553, l. 8. For > read ⩾.