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1. CMB 2011 (vol 54 pp. 757)
Cancellation of Cusp Forms Coefficients over Beatty Sequences on $\textrm{GL}(m)$ Let $A(n_1,n_2,\dots,n_{m-1})$
be the normalized Fourier coefficients of
a Maass cusp form on $\textrm{GL}(m)$.
In this paper, we study the cancellation of $A
(n_1,n_2,\dots,n_{m-1})$ over Beatty sequences.
Keywords:Fourier coefficients, Maass cusp form on $\textrm{GL}(m)$, Beatty sequence Categories:11F30, 11M41, 11B83 |
2. CMB 2008 (vol 51 pp. 508)
A Result in Surgery Theory We study the topological $4$-dimensional surgery problem
for a closed connected orientable
topological $4$-manifold $X$ with vanishing
second homotopy and $\pi_1(X)\cong A * F(r)$, where $A$ has
one end and $F(r)$ is the free group of rank $r\ge 1$.
Our result is related to a theorem of Krushkal and Lee, and
depends on the validity of the Novikov conjecture for
such fundamental groups.
Keywords:four-manifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map Categories:57N65, 57R67, 57Q10 |
3. CMB 1999 (vol 42 pp. 274)
The Bockstein Map is Necessary We construct two non-isomorphic nuclear, stably finite,
real rank zero $C^\ast$-algebras $E$ and $E'$ for which
there is an isomorphism of ordered groups
$\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to
\bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible
with all the coefficient transformations. The $C^\ast$-algebras
$E$ and $E'$ are not isomorphic since there is no $\Theta$
as above which is also compatible with the Bockstein operations.
By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair
of non-isomorphic, real rank zero, purely infinite $C^\ast$-algebras
with similar properties.
Keywords:$K$-theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$-algebras, real rank zero, purely infinite, classification Categories:46L35, 46L80, 19K14 |
4. CMB 1999 (vol 42 pp. 285)
On Kloosterman Sums with Oscillating Coefficients In this paper we prove: for any positive integers $a$ and $q$ with
$(a,q) =1$, we have uniformly
$$
\sum_{\substack{n \leq N \\ (n,q) = 1, \,n\on \equiv 1 (\mod q)}}
\mu (n) e \left( \frac{a\on}{q} \right) \ll Nd (q) \left\{
\frac{\log^{\frac52} N}{q^{\frac12}} + \frac{q^{\frac15}
\log^{\frac{13}5} N}{N^{\frac15}} \right\}.
$$
This improves the previous bound obtained by D.~Hajela,
A.~Pollington and B.~Smith~\cite{5}.
Keywords:Kloosterman sums, oscillating coefficients, estimate Category:10G10 |