Abstract We study non-vanishing of Dirichlet L -functions at the central point under unlikely assumption that there exists an exceptional character. In particular we prove if $$\psi $$ ψ is a real primitive character modulo $$D \in \mathbb {N}$$ D ∈ N</mml:...

‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals) is topologized.

Let R be a ring with an automorphism σ. An ideal I of R is σ-ideal of R if σ(I) = I. A proper ideal P of R is σ-prime ideal of R if P is a σ-ideal of R and for σ-ideals I and J of R, IJ ⊆ P implies that I ⊆ P or J ⊆ P . A proper ideal Q of R is σ-semiprime ideal of Q if Q is a σ-ideal and for a σ-ideal I of R, I2 ⊆ Q implies that I ⊆ Q. The σ-prime radical is defined by the intersection of all ...

Let d ≥ 3 be an integer and p a prime coprime to d. Let Q and Qp be the algebraic closure of Q and Qp respectively. Let Zp be the ring of integers of Qp. Suppose f(x) is a degree-d polynomial in (Q ∩ Zp)[x]. Let Q(f) be the number field generated by coefficients of f in Q. Let P be a prime ideal in the ring of integers OQ(f) of Q(f) lying over p, with residue field Fq for some p-power q. Let A ...

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

It is well-known that two modular forms on the same congruence subgroup and of the same weight, with coefficients in the integer ring of a number field, are congruent modulo a prime ideal in this integer ring, if the first B coefficients of the forms are congruent modulo this prime ideal, where B is an effective bound depending only on the congruence subgroup and the weight of the forms. In thi...

In [4] B. M. Schein considered systems of the form ( ; o; n),where is a set of functions closed under the composition "o" of functions (and hence ( ; o) is a function semigroup) and the set theoretic subtraction "n" (and hence is a subtraction algebra in the sense of [1]). He proved that every subtraction semigroup is isomorphic to a di erence semigroup of invertible functions. B. Zelinka [5] d...

Inspired by the recent observation of a new structure, $X(4014)$, in process $\gamma\gamma\to \gamma\psi(2S)$, we evaluate possibility assigning $X(4014)$ as $D^\ast \bar{D}^\ast$ molecular state with $I(J^{PC})=0(0^{++})$ investigating hidden charm decays $X(4014)$. The partial widths $J/\psi\omega$, $ \eta_{c}\eta$ and $\eta_{c}\eta^{\prime}$ channels are evaluated to be about $(0.41\sim 5.00...