1. CMB Online first
 Lü, Guangshi; Sankaranarayanan, Ayyadurai

Higher Moments of Fourier Coefficients of Cusp Forms
Let $S_{k}(\Gamma)$ be the space of holomorphic cusp
forms of even integral weight $k$ for the full modular group
$SL(2, \mathbb{Z})$. Let
$\lambda_f(n)$, $\lambda_g(n)$, $\lambda_h(n)$ be the $n$th normalized
Fourier
coefficients of three distinct holomorphic primitive cusp forms
$f(z) \in S_{k_1}(\Gamma), g(z) \in S_{k_2}(\Gamma), h(z) \in
S_{k_3}(\Gamma)$ respectively.
In this paper we study the cancellations of sums related to arithmetic
functions, such as $\lambda_f(n)^4\lambda_g(n)^2$, $\lambda_g(n)^6$,
$\lambda_g(n)^2\lambda_h(n)^4$, and $\lambda_g(n^3)^2$ twisted
by
the arithmetic function $\lambda_f(n)$.
Keywords:Fourier coefficients of automorphic forms, Dirichlet series, triple product $L$function, Perron's formula Categories:11F30, 11F66 

2. CMB Online first
 Williams, Kenneth S.

Ternary quadratic forms and eta quotients
Let $\eta(z)$ $(z \in \mathbb{C},\;\operatorname{Im}(z)\gt 0)$
denote the Dedekind eta function. We use a recent producttosum
formula in conjunction with conditions for the nonrepresentability
of integers by certain ternary quadratic forms to give explicitly
10 eta quotients
\[
f(z):=\eta^{a(m_1)}(m_1 z)\cdots \eta^{{a(m_r)}}(m_r z)=\sum_{n=1}^{\infty}c(n)e^{2\pi
i nz},\quad z \in \mathbb{C},\;\operatorname{Im}(z)\gt 0,
\]
such that the Fourier coefficients $c(n)$ vanish for all positive
integers $n$ in each of infinitely many nonoverlapping arithmetic
progressions. For example, it is shown that for $f(z)=\eta^4(z)\eta^{9}(4z)\eta^{2}(8z)$
we have $c(n)=0$ for all $n$ in each of the arithmetic progressions
$\{16k+14\}_{k \geq 0}$, $\{64k+56\}_{k \geq 0}$, $\{256k+224\}_{k
\geq 0}$, $\{1024k+896\}_{k \geq 0}$, $\ldots$.
Keywords:Dedekind eta function, eta quotient, ternary quadratic forms, vanishing of Fourier coefficients, producttosum formula Categories:11F20, 11E20, 11E25 

3. CMB 2011 (vol 54 pp. 757)
 Sun, Qingfeng

Cancellation of Cusp Forms Coefficients over Beatty Sequences on $\textrm{GL}(m)$
Let $A(n_1,n_2,\dots,n_{m1})$
be the normalized Fourier coefficients of
a Maass cusp form on $\textrm{GL}(m)$.
In this paper, we study the cancellation of $A
(n_1,n_2,\dots,n_{m1})$ over Beatty sequences.
Keywords:Fourier coefficients, Maass cusp form on $\textrm{GL}(m)$, Beatty sequence Categories:11F30, 11M41, 11B83 

4. CMB 2008 (vol 51 pp. 508)
 Cavicchioli, Alberto; Spaggiari, Fulvia

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:fourmanifolds, homotopy type, obstruction theory, homology with local coefficients, surgery, normal invariant, assembly map Categories:57N65, 57R67, 57Q10 

5. CMB 1999 (vol 42 pp. 274)
 Dădărlat, Marius; Eilers, Søren

The Bockstein Map is Necessary
We construct two nonisomorphic 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 nonisomorphic, 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 

6. CMB 1999 (vol 42 pp. 285)
 Deng, Peiming

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 
