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The lattices of eightand ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in GL„(Z) for n = 8, 10, are classified in this paper. The number of types is 52 in the case n = 8 , and 47 in the case n = 10. As a consequence of this classification one has 26, resp. 46, conjugacy classes of maximal finite irreducible subgroups ...

One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.

‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

Klein’s modular j-function is defined to be j(z) = E 4/Δ(z) = 1 q + 744 + ∞ ∑ n=1 c(n)q where z ∈ C with (z) > 0, q = exp(2iπz), E4(z) denotes the normalized Eisenstein series of weight 4 and Δ(z) is the Ramanujan’s Delta function. In this short note, we show that for each integer a ≥ 1, the interval (a, 4a(a+1)) (respectively, the interval (16a−1, (4a+1)2)) contains an integer n with n ≡ 7 (mo...

Let UZ(n) be the minimal rank of n-universal Z-lattices, by which we mean positive definite Z-lattices which represent all positive Z-lattices of rank n. It is a well known fact that UZ(n) = n + 3 for 1 ≤ n ≤ 5. In this paper, we determine UZ(n) and find all n-universal lattices of rank UZ(n) for 6 ≤ n ≤ 8.

‎in this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of malmquist type‎ $$‎sum^n_{j=1}f(z+c_j)=frac{p(f(z))}{q(f(z))}‎,$$ ‎where $n(in{mathbb{n}})geq{2}$‎, ‎and $p(f(z))$ and $q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎moreover‎, ‎the properties of finite o...