Related papers: A generalization of Tur\'{a}n's theorem

We generalize the theory of ordering character triples, developed by Navarro and Sp\"ath, by taking into account the action of Galois automorphisms on characters. This new technique, together with previous results of Ladisch and Turull,…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We generalized the Lodha-Moore group into $n$-adic and showed analogues in the Lodha-Moore group of properties between the Thompson group $F$ and the generalized Thompson group $F(n)$.

In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We apply Vaaler's lemma and the Erd\H{o}s-Turan inequality to…

We prove a generalized Gauss-Kuzmin-L\'evy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.

We prove an analogue of the Centralizer Theorem in the context of Artin-Tits groups.

We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and short alternative to Katsuura's proof of this generalization.

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.

We prove Abelian and Tauberian theorems for regularised Cauchy transforms of positive Borel measures on the real line whose distribution functions grow at most polynomially at infinity. In particular, we relate the asymptotics of the…

A proof of Sendov's conjecture is given.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.

We derive an asymptotic expansion with effective error bound for $u(n)$, counting the number of unimodal sequences of size $n$. We prove that $u(n)$ satisfies the higher order Tur\'{a}n inequalities for $n\geq33$ and that certain second…

We show that the normalised ultraspherical polynomials, $G_n^{(\lambda)}(x)=C_n^{(\lambda)}(x)/C_n^{(\lambda)}(1)$, satisfy the following stronger version of Tur\'{a}n inequality, $$|x|^\theta \left(G_n^{(\lambda)}(x)\right)^2…

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

In this article we explain the Buium--Coleman approach to the Manin--Mumford conjecture, and outline its generalisations. As an illustration, we give a $p$-adic proof of a theorem of Bombieri, Masser and Zannier on curves in tori.

We present a proof of the Sturm-Hurwitz theorem, using basic calculus.

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.