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Displaying 1361 – 1380 of 3028

On some Extremal Problems of Landau

Révész, Szilárd (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.The prime number theorem with error term presents itself as &pi'(x) = ∫2x [dt/ logt] + O ( x e- K logL x). In 1909, Edmund Landau provided a systematic analysis of the proof seeking better values of L and K. At a key point of his 1899 proof de la Vallée Poussin made use of the nonnegative trigonometric polynomial 2/3 (1+cos x)2 = 1+4/3 cosx +1/3 cos2x. Landau considered more general positive definite nonnegative...

On some Formulas Involving !n and the Verification of the !n-hypothesis by use of Computers

Žarko Mijajlović (1990)

Publications de l'Institut Mathématique

On some general problems in the theory of partitions, I

P Erdös, P. Turán (1971)

Acta Arithmetica

On some generalizations of the diophantine equation $1^{k} + 2^{k} + . . . + x^{k} = y^{z}$

B. Brindza (1984)

Acta Arithmetica

On some generalizations of the diophantine equation $s (1^{k} + 2^{k} + \dots + x^{k}) + r = d y^{n}$

Csaba Rakaczki (2012)

Acta Arithmetica

On Some Hasse Principles over Formally Real Fields.

Alexander Prestel, Richard Elman, Tsit-Yuen Lam (1973)

Mathematische Zeitschrift

On some identities for the Fibonomial coefficients

Jaroslav Seibert, Pavel Trojovský (2005)

Mathematica Slovaca

On some imaginary triquadratic number fields $k$ with ${Cl}_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2021)

Commentationes Mathematicae Universitatis Carolinae

Let $d$ be a square free integer and $L_{d} : = ℚ (ζ_{8}, \sqrt{d})$ . In the present work we determine all the fields $L_{d}$ such that the $2$ -class group, ${Cl}_{2} (L_{d})$ , of $L_{d}$ is of type $(2, 4)$ or $(2, 2, 2)$ .

On some inequalities concerning $π (x)$ .

Garunkštis, R. (2002)

Experimental Mathematics

On some inequalities connected with Fermat's equation.

Krystyna Bialek (1988)

Elemente der Mathematik

On Some Integrals Involving the Mean Square Formula for the Riemann Zeta-function

Aleksandar Ivić (1989)

Publications de l'Institut Mathématique

On some invariants for systems of quadratic forms over the integers.

Jorge Morales (1992)

Journal für die reine und angewandte Mathematik

On some issues concerning polynomial cycles

Tadeusz Pezda (2013)

Communications in Mathematics

We consider two issues concerning polynomial cycles. Namely, for a discrete valuation domain $R$ of positive characteristic (for $N \geq 1$ ) or for any Dedekind domain $R$ of positive characteristic (but only for $N \geq 2$ ), we give a closed formula for a set $𝒞 Y C L (R, N)$ of all possible cycle-lengths for polynomial mappings in $R^{N}$ . Then we give a new property of sets $𝒞 Y C L (R, 1)$ , which refutes a kind of conjecture posed by W. Narkiewicz.

On some Kloosterman sums.

Stefan Kühnlein (1991)

Manuscripta mathematica

On some Markov matrices arising from the generalized Collatz mapping

R. Buttsworth, K. Matthews (1990)

Acta Arithmetica

On some mean value results for the zeta-function in short intervals

Aleksandar Ivić (2014)

Acta Arithmetica

Let $Δ (x)$ 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 $\int_{0}^{T} E * (t) d t = 3 / 4 π T + R (T)$ , 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 dt $(k \in ℕ, 1 ≪ H \leq T)$ are...

On some mean value results involving |zeta(1/2+ it)|

A. Ivić (2003)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

On some mean value results involving $| ζ (1 / 2 + i t) |$ .

Ivić, A. (2003)

Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques

On some metabelian 2-groups and applications I

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Colloquium Mathematicae

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 $G a l (k ₂^{(2)} / k) ≃ G$ , where $k ₂^{(2)}$ is the second Hilbert 2-class field of k.

On some modifications of two theorems of Erdős

Katalin Kovács (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

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