This list of errata is also available as a plain tex file or a tex dvi file.

**Note:** a negative line number is a line number counted upwards from
the bottom of the page.

- p.4, line 8. `re' should not be italicized.
- p.6, bottom. The hypotheses on f do not imply that F is of locally bounded variation. Therefore add the hypothesis that f is of bounded total variation. This is true, for example, if f(x) is monotone for |x| large.
- p.9, fourth displayed formula (Fourier Inversion Formula). Omit subscript of t.
- p.11, line 7. ``Now substituting (1.19) ....'' It is not (1.19) which is substituted, but rather the formula at the bottom of p.10.
- p.18, line 12: omit space in `Z/ NZ'.
- p.19, line -10. Missing closing absolute value sign in |re(gamma(z))|<=1/2.
- p.20, formula (2.3). Comma should be outside the matrix.
- p.20, proof of Proposition 1.2.3. The bar is used in two different ways, which could be confusing. In the second usage (bar of gamma(F)) it means the topological closure.
- p.29, second displayed formula. The coefficient of q^5 should be 4830, not 2954.
- p.32, comments after Proposition 1.3.5. The estimate should be a_n <= Cn^{(k-1)/2+epsilon} for any positive epsilon.
- p.35, bottom. $H^1$ and $H^2$ should be $H_1$ and $H_2$.
- p.41, l. -10. In the Fourier expansion, the exponent of e should be multiplied by z.
- p.49, last line of proof of Theorem 1.4.4, Eq.(4.10) should be Eq.(4.11).
- p.52, Exercise 1.4.13, displayed formula. The last exponent of p should be k-1-2s, not -2s.
- p.52, bottom. Theorem 1.4.4 should be Theorem 1.4.5.
- p.53, line 11. ``theoretic'' should not be repeated.
- p.57, last line. (3.14) should be (3.16).
- p.58, line 2. Theorem 1.4.3 should be Theorem 1.4.4.
- p.60, beginning of paragraph before Theorem 1.5.1, `f in Gamma_0(N)' should be `f in S_k(Gamma_0(N),psi)'.
- p.66, third line from end of proof, ``follows from Eq. (6.5)'' should be ``follows from Eq. (6.6).
- p.67, after third displayed formula, omit the unnecessary ``... and the subsequent evaluation of the constant c.''
- p.69, bottom and p.71, first formula, infinity sign should be a subscript of Gamma.
- p.70, statment of Proposition 1.6.1, ``most simple poles'' should be ``at most simple poles.''
- p.72, first displayed formula: omit i in exponential.
- p.72, after statement of Theorem 1.6.2, (3.11) should be (3.13).
- p.74, line 3. Proposition 1.6.3 should be Theorem 1.6.2.
- p.76, line 2. Do not italicize ``re.''
- p.77, line 17. ``resulting the assumption from'' should be ``resulting from the assumption.''
- p.77, next to last line. The tensor product symbol should not be there: the index is supposed to be [o^x:o^x_+].
- p.90, Exercise 1.7.2. Insert space before (7.6).
- p.108. It is asserted that the Laplacian is positive definite. This should be ``semidefinite,'' and the reference should be to Exercise 2.1.8.
- p.129, first displayed formula, second partial derivative is with respect to z-bar, not z.
- p.129, (1.2) at bottom. In the definition of L_k, the partial derivative should be with respect to z-bar, not z.
- p.131, l. -12, the fraktur (German) h should be lower case.
- p.135, p.135, proof of Lemma 2.1.2. Not really an error, but replace ``closed manifold'' by ``compact manifold.''
- p.135, l. -4. In ``omega=u+iv=...'' omega should be w.
- p.170, Proposition 2.3.1 (iii), after the backslashes, insert G (twice).
- p.188, line 6. The function pi(g) Xf is automatically continuous, so this does not need to be assumed.
- p.245, near bottom. Replace X by D in this discussion, and note that pi(D)f is defined by (4.1) when D=X is in the Lie algebra g, and extended to U(g) by Proposition 2.2.3.
- p.291, line 16. L^2 should be L^2_0.
- p.310, line -8. Amend this to read: ``We will call H_G the Hecke algebra of G.''
- p.312, line 3. Amend this to read ``According to the notes in Knapp and Vogan, Flath had originally ...''
- p.317, line -11. ``This is a generalization of Theorem IV.6.6'' should read ``Theorem 4.6.3.'' Any theorem or proposition with a roman numeral should be suspected of being wrong. Let me know if you find any others!
- p.321, Theorem 3.5.1. The functional is of course only unique up to constant multiple.
- p.322, statement of Theorem 3.5.2. Add the assumption that (pi,V) is admissible.
- p.375, ``metaplectid'' should be ``metaplectic.''
- p.379, table. In the third (L-group) column n should be n+1 for the first three entries.
- p.383, line 21. ``hat pi is the Langlands L-function'' should be ``L(s,hat pi) is the Langland L-function.''
- p.383, l.-4 and -3. GL(2) should be GL(n) (twice) and GL(8) should be GL(n^2-1) (three times).
- p.385, Third line from bottom. (pi_1,V_0) should be (pi_1,V_1).
- p.426, formula (2.2). Omit parentheses from d_L(b); similarly, omit parenthesis from d_L(g) in following displayed formula.
- p.432. Not a correction, but it is useful to know that a stronger result than Proposition 4.2.7 is true. If there exists a single open subgroup K such that V_1^K and V_2^K are nonzero (hence simple H_K modules by Proposition 4.2.3), and if these are isomorphic as H_K modules, then V_1 and V_2 are isomorphic. To prove this, adapt the proof of Theorem 4.6.3 on p.493.
- p.436, second sentence of Section 4.3, ``this result'' should be ``these topics.''
- p.486, last displayed formula and p.487, top displayed formula. Domain of integration should be p^(-N).
- p.488, first displayed formula. The definition of L_2 is slightly
wrong. The second term phi(1) should be multiplied by a function
h(x) designed to make the statement that the integral is compactly
supported actually true! For example, we can take:

h(x)=|x|^-1 (chi_1^-1 chi_2)(x) if |x|>1 0 if |x|<=1

- p.493, Theorem 4.6.3. Not a correction, but note that this is a special case of the generalization of Proposition 4.2.7 described above on the note to p.432.
- p.540, line 14. Amend this to read ``After partial results towards Howe's conjecture were obtained by Howe and other authors, the conjecture was fully proved for local fields of odd residue characteristic by Waldspurger (1990).''
- p.541, Theorem 4.8.6. Since it is assumed here that E is a field, delete all references to the case E=F+F in the statement and proof of this theorem! The case where E=F+F is considered separately, later.
- p.550. The discussion in the second paragraph switches from GL(2) to GL(n) in a confusing way. Amend the third and fourth sentences to read ``The conjecture includes a hypothetical classification of the irreducible admissible representations of GL(n,F), where F is a local field, which has been proved in many cases. Over an archimedean field, the local Langlands conjecture (for an arbitrary reductive group) is a theorem of Langlands.''
- p.557, last paragraph. ``Theorem 4.9.3'' should be ``Proposition 4.9.3,'' and ``Theorem 4.9.4'' should be ``Theorem 4.9.1.''
- p.560. The paper of Doi and Naganuma was in vol. 9 of Inventiones, not vol. 19.

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