Expand all Collapse all | Results 1 - 6 of 6 |
1. CMB 2012 (vol 56 pp. 544)
Universally Overconvergent Power Series via the Riemann Zeta-function The Riemann zeta-function is employed to generate universally overconvergent power series.
Keywords:overconvergence, zeta-function Categories:30K05, 11M06 |
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 2008 (vol 51 pp. 627)
Summation of Series over Bourget Functions In this paper we derive formulas for summation of series involving
J.~Bourget's generalization of Bessel functions of integer order, as
well as the analogous generalizations by H.~M.~Srivastava. These series are
expressed in terms of the Riemann $\z$ function and Dirichlet
functions $\eta$, $\la$, $\b$, and can be brought into closed form in
certain cases, which means that the infinite series are represented
by finite sums.
Keywords:Riemann zeta function, Bessel functions, Bourget functions, Dirichlet functions Categories:33C10, 11M06, 65B10 |
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 2003 (vol 46 pp. 546)
$L$-Series of Certain Elliptic Surfaces In this paper, we study the modularity of certain elliptic surfaces
by determining their $L$-series through their monodromy groups.
Categories:14J27, 11M06 |
6. CMB 1999 (vol 42 pp. 263)
Mellin Transforms of Mixed Cusp Forms We define generalized Mellin transforms of mixed cusp forms, show
their convergence, and prove that the function obtained by such a
Mellin transform of a mixed cusp form satisfies a certain
functional equation. We also prove that a mixed cusp form can be
identified with a holomorphic form of the highest degree on an
elliptic variety.
Categories:11F12, 11F66, 11M06, 14K05 |