On some inequalities concerning .
On some inequalities connected with Fermat's equation.
On Some Integrals Involving the Mean Square Formula for the Riemann Zeta-function
On some invariants for systems of quadratic forms over the integers.
On some issues concerning polynomial cycles
We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain of positive characteristic (for ) or for any Dedekind domain of positive characteristic (but only for ), we give a closed formula for a set of all possible cycle-lengths for polynomial mappings in . Then we give a new property of sets , which refutes a kind of conjecture posed by W. Narkiewicz.
On some Kloosterman sums.
On some Markov matrices arising from the generalized Collatz mapping
On some mean value results for the zeta-function in short intervals
Let denote the error term in the Dirichlet divisor problem, and let E(T) denote the error term in the asymptotic formula for the mean square of |ζ(1/2+it)|. If E*(t) := E(t) - 2πΔ*(t/(2π)) with Δ*(x) = -Δ(x) + 2Δ(2x) - 1/2Δ(4x) and , then we obtain a number of results involving the moments of |ζ(1/2+it)| in short intervals, by connecting them to the moments of E*(T) and R(T) in short intervals. Upper bounds and asymptotic formulae for integrals of the form ∫T2T(∫t-Ht+H |ζ(1/2+iu|2 duk dtare...
On some mean value results involving |zeta(1/2+ it)|
On some mean value results involving .
On some metabelian 2-groups and applications I
Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
On some modifications of two theorems of Erdős
On some new congruences for generalized Bernoulli numbers
On some new estimates for h¯(ℚ(ζₚ))
On some non-holonomic sequences.
On some number-theoretic sums introduced by Jacobsthal
On Some Partition Functions Related to Some Mock Theta Functions
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
On some partitions related to .
On some permutation polynomials over finite fields.
On some polynomials allegedly related to the abc conjecture