Expand all Collapse all | Results 1 - 5 of 5 |
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 2011 (vol 54 pp. 316)
The Saddle-Point Method and the Li Coefficients
In this paper, we apply the saddle-point method in conjunction with
the theory of the NÃ¶rlund-Rice integrals to derive precise
asymptotic formula for the generalized Li coefficients established
by Omar and Mazhouda.
Actually, for any function $F$ in the Selberg class
$\mathcal{S}$ and under the Generalized Riemann Hypothesis, we have
$$
\lambda_{F}(n)=\frac{d_{F}}{2}n\log n+c_{F}n+O(\sqrt{n}\log n),
$$
with
$$
c_{F}=\frac{d_{F}}{2}(\gamma-1)+\frac{1}{2}\log(\lambda
Q_{F}^{2}),\ \lambda=\prod_{j=1}^{r}\lambda_{j}^{2\lambda_{j}},
$$
where $\gamma$ is the Euler's constant and the notation is as below.
Keywords:Selberg class, Saddle-point method, Riemann Hypothesis, Li's criterion Categories:11M41, 11M06 |
3. CMB 2007 (vol 50 pp. 11)
van der Pol Expansions of L-Series We provide concise series representations for various
L-series integrals. Different techniques are needed below and above
the abscissa of absolute convergence of the underlying L-series.
Keywords:Dirichlet series integrals, Hurwitz zeta functions, Plancherel theorems, L-series Categories:11M35, 11M41, 30B50 |
4. CMB 2004 (vol 47 pp. 468)
Strong Multiplicity One for the Selberg Class We investigate the problem of determining elements in the Selberg
class by means of their Dirichlet series coefficients at primes.
Categories:11M41, 11M26, 11M06 |
5. CMB 1997 (vol 40 pp. 364)
On the non-vanishing of a certain class of Dirichlet series In this paper,
we consider Dirichlet series with Euler products of the form
$F(s) = \prod_{p}{\bigl(1 + {a_p\over{p^s}}\bigr)}$ in $\Re(s) > 1$,
and which are regular in $\Re(s) \geq 1$ except for a pole of
order $m$ at $s = 1$.
We establish criteria for such a Dirichlet series to be non-vanishing
on the line of convergence. We also show that our results
can be applied to yield non-vanishing results for a subclass of the
Selberg class and the Sato-Tate conjecture.
Categories:11Mxx, 11M41 |