Related papers: From Rolle's theorem to the Sturm-Hurwitz theorem

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S$^1$, S$^3$ and S$^7.$ In this process, we discovered the analogue of Hurwitz theorem for curved spaces and a geometrical…

In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.

In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.

We show the integrality of the simple Hurwitz numbers. The main tool is the cut-and-join operator, and our proof is a purely combinatorial one.

We obtain another proof of Hermite's integral for the Hurwitz zeta function.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.

In this paper we announce some results obtained for certain algebraic functions, which we call of cyclotomic type. The main results properly resemble von Staudt-Clausen's theorem and Kummer's congruence for the Bernoulli numbers, and such…

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

By Probability theory, that is, by a kind of quasi-law of the iterated logarithm, we prove the title claim.

A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a…

We give a short and direct proof of the $\lambda_g$-Conjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the ``polynomiality'' of Hurwitz numbers, from which we pick off the lowest degree…

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

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