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Search: MSC category 11M06 ( $\zeta (s)$ and $L(s, \chi)$ )

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1. CMB 2012 (vol 56 pp. 544)

Gauthier, P. M.
 Universally Overconvergent Power Series via the Riemann Zeta-function The Riemann zeta-function is employed to generate universally overconvergent power series. Keywords:overconvergence, zeta-functionCategories:30K05, 11M06

2. CMB 2011 (vol 54 pp. 316)

Mazhouda, Kamel
 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 criterionCategories:11M41, 11M06

3. CMB 2008 (vol 51 pp. 627)

Vidanovi\'{c}, Mirjana V.; Tri\v{c}kovi\'{c}, Slobodan B.; Stankovi\'{c}, Miomir S.
 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 functionsCategories:33C10, 11M06, 65B10

4. CMB 2004 (vol 47 pp. 468)

Soundararajan, K.
 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)

Long, Ling
 $L$-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)

Choie, Youngju; Lee, Min Ho
 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