# The relaxed Dirichlet energy of mappings into a manifold

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We give explicit upper bounds for |L(1,?)|for primitive Dirichlet characters ?. These bounds depend on the behaviour of ?at primes p in a given set S of primes.

- On the Stability of the Maximum Term of the Entire Dirichlet Series. Skaskiv, O.; Trakalo, O. // Ukrainian Mathematical Journal;Apr2005, Vol. 57 Issue 4, p686
We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series $$F(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n e^{z\lambda _n } }$$ and $$B(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n b_n e^{z\lambda _n } }$$ to be asymptotically...

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The Dirichlet boundary-value problem for the eigenvalues of the LamÃ© operator in a twodimensional bounded domain with a small hole is studied. The asymptotics of the eigenvalue of this boundary-value problem is constructed and justified up to the power of the parameter defining the diameter...

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Using a variational approach, we prove the existence of solutions for the degenerate quasilinear elliptic system -div(v1(x)|âˆ‡u|p-2âˆ‡u) = Î»Fu(x, u, v) + ÂµGu(x, u, v), -div(v2(x)|âˆ‡v|q-2âˆ‡v) = Î»Fv(x, u, v) + ÂµGv(x, u, v), with Dirichlet boundary conditions.

- On the hybrid mean value of a sum analogous to character sum over quarter interval. REN Gang-lian // Basic Sciences Journal of Textile Universities / Fangzhi Gaoxia;mar2014, Vol. 27 Issue 1, p5
Two kinds of hybrid mean value of a sum analogous to character sums over quarter interval are studied. By transforming the sum into a sum involving Gauss sums and Dirichlet L-functions, then using the properties of primitive character and estimates of Dirichlet L-f unctions, some sharper...

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To a finitely generated profinite group $G$, a formal Dirichlet series $P_G(s)\,{=}\,\sum_{n}{a_n}/{n^s}$ is associated, where $a_n \,{=}\,\sum_{|G:H|=n} \mu_G(H)$. It is proved that $G$ is prosoluble if and only if the sequence $\{a_n\}_{n \in \mathbb...

- On the zeros of the L-function associated with the cubic theta function. Proskurin, N. // Journal of Mathematical Sciences;May2008, Vol. 150 Issue 3, p2105
The paper considers the function defined by the Dirichlet series , where t(?) is the ?th Fourier coefficient of the cubic Kubota-Patterson theta function. The zeros of the function L(t ï¿½) in the domain |Im s| < 444 are computed. Bibliography: 4 titles.

- A Combined Method for Calculating the Field of a Point Source in a Waveguide (Plane-Layered Media). Philippov, V.; Kirpichnikova, N.; Vlasyuk, N. // Journal of Mathematical Sciences;Jan2006, Vol. 132 Issue 1, p113
The two-dimensional problem of propagating the waves generated by a point source, in a depth plane-layered waveguide is investigated. The Dirichlet condition is given on the boundary of the waveguide and also two consistency conditions are defined on the interface between the fluid and the...