Department of Mathematics and Statistics Boston University Boston, MA 02215 (617) 353-9545 rohrlich@math.bu.edu.
1. Self-dual Artin representations 2. Artin representations of Q of dihedral type 3. Quaternionic Artin representations of Q 4. Appendix to: A. Karnataki, Self-dual Artin representations of dimension three 5. A Taniyama product for the Riemann zeta function 6. Almost abelian Artin representations of Q 7. Quaternionic Artin representations and nontraditonal arithmetic statistics 8. Dihedral Artin representations and CM fields 9. Multiplicities in Mordell-Weil groups 10. Average multiplicities
Quaternionic Artin representaions and nontraditional
arithmetic statistics ,
Transactions of the AMS 372 (2019), 8587-8603.
These aren't strictly speaking errors, but I will list them here
because I don't want to create a separate category for imbecilities:
In the displayed presentation for $D_{2m}$ on p. 8587,
there is no need to state the relation $a^m=1$ twice (although
I suppose there is some value in contrasting the presentation with
that of $Q_{4m}$). Also, at the end of the sentence containing
displayed formula (2) on p. 8588, $1/4\sqrt{e}$ should
have been written $1/(4\sqrt{e})$.
Quaternionic Artin representations of Q ,
Math. Proc. Cambridge Phil. Soc. 163 (2017), 95-114.
In the first paragraph of the introduction, the
asymptotic relation proved by Klueners is misstated:
It should be $Z(k,G;x)\sim cx^a$
with a positive constant $c$.
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.
The following errors have been corrected in the above pdf file
but disfigure the published version:
(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 $K=F(\varpi^{1/e})$.
Almost abelian Artin representations of Q . Michigan Math. J. 68 (2019), 127--145. (2017). Although I referred to Serre's paper [11], I overlooked the fact that Corollary 2 on p. 143 was an immediate consequence of formula (220) in Serre's subsequent paper on applications of the Chebotarev density theorem (see p. 624 of Volume III of Serre's Collected Papers).
A Taniyama product for the Riemann zeta function. In: Exploring the Riemann Zeta Function: 190 Years from Riemann's Birth, H. Montgomery, A. Nikeghbali, and M. Rassias eds., Springer (2017). I deeply apologize for being completely unaware of, and hence not acknowledging, the following prior literature: [1] K. Joshi, R. Ragunathan, Infinite product identities for L-functions, Illinois J. Math. 49 (2005), 885-891. [2] K. Joshi, C. S. Yogananda, A remark on products of Dirichlet L-functions, Acta Arith. 91 (1999), 325-327. [3] J. Kaczorowski, A. Perelli, Some remarks on infinite products of L-functions, J. Math. Anal. and Appl. 406 (2013), 293-298. In particular, Kaczorowski and Perelli consider product identities for a vastly more general class of L-functions, the identity for $1/\zeta(s)$ being merely a special case. I am grateful to Alberto Perelli for drawing my attention to the above literature and for showing me a proof of Theorem 2 valid for the subclass of Euler products in [3] which are of "polynomial type."