Department of Mathematics and Statistics

Boston University

Boston, MA 02215

(617) 353-9545

rohrlich@math.bu.edu.

Inductivity of the global root number

*Self-dual Artin representations*. In:
*Automorphic Representation and L-functions*,
D. Prasad, C.S. Rajan, A. Sankaranarayanan, J. Sengupta, eds.,
Tata Institute of Fundamental Research Studies in Mathematics Vol. 22
(2013), 455 -- 499.

(i) The sentence following (4.1) on p. 465 should be corrected as follows:
"Indeed let `$m$`

be a positive integer not divisible by 4 such
that the greatest common divisor of `$m$`

and the discriminant of
`$F$`

divides 2, and let ..."
(ii) In the second line from the bottom of p. 472, `$\mathfrak q$`

should be `$q$`

.
(iii) The constant in the asymptotic
relation (9.3) on p. 487 is incorrect, both because of double-counting and
because the formula for `$q(\rho)$`

holds in general only if `$q(\psi)$`

is
relatively
prime to `$d_K$`

. However, the bound
`$\vartheta^{\ab, K}_{\Q,2}(x) \ll x$`

still holds,
and if (9.3) is replaced by this bound then the rest of the argument goes
through as before.

*A deformation of the Tate module*,
J. of Algebra 229 (2000), 280 -- 313.

The formula for ` $\theta(c)$ `

on p. 294 is in error:
The coefficient of ` $X^2$ `

should be
` $(c^4-c^2)/12$, `

not ` $(c^4+2c^2-3c)/24$. `

Although very embarrassing,
the error is inconsequential in the sense that there
was no need to display the coefficient of ` $X^2$ `

in the first place.

*Galois theory, elliptic curves, and root numbers*,
Compositio Math. (1996), 311 -- 349.

In the first line of the paragraph containing displayed formula
(3.6) on p. 331, the equation ` $K=F(\Delta^{1/e})$`

should be ` $K=F(\varpi^{1/e})$`

.