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.