1. CMB 2015 (vol 58 pp. 858)
 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 

2. CMB 2015 (vol 58 pp. 548)
 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 

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 
