Related papers: Analytic Bertini theorem
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
We prove a uniformization theorem in complex algebraic geometry.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
We prove a generalization of the Hasumi's Direct Cauchy Theorem property for the derivatives (Theorem 2.2).
We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreducibility theorem.
In this note we give a detailed proof of a theorem of Aubin.
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of their proofs, we obtain some combinatorial results.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
In this paper, we show a generalized Join theorem for real analytic singularities. For complex singularities, this theorem was proved by A. N\'emethi.
We prove a semiample generalization of Poonen's Bertini Theorem over a finite field that implies the existence of smooth sections for wide new classes of divisors. The probability of smoothness is computed as a product of local…
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
A generalization of the law of total covariance is presented and proved.
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
We generalize Rado's extension theorem to complex spaces.
We show the existence of a hypersurface that contains a given closed subscheme of a projective space over a finite field and intersects a smooth quasi-projective scheme smoothly, under some condition on the dimension. This generalizes a…
We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions
We present a new, elementary, dynamical proof of the prime number theorem.