Related papers: Simple Proofs of the Variational and Multiple Prio…
We present a new, elementary, dynamical proof of the prime number theorem.
We provide a simple proof of a generalization of the multivariate Chu-Vandermonde identity recently derived in Favaro et al. (2010a). Exploiting known results for rising factorials and fourth Lauricella polynomials we show resorting to…
We proved three theorems of $S$-version of the mulyiplicity one.
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
This is the English translation, done by Yihang Zhu, of the paper by Langlands and Rapoport, originally published in J. Reine Angew. Math. 378 (1987), pages 113-220. The translator also added some historical notes.
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
In this paper we present the initial development of a general theory for mapping inference in predicate logic to computation over Tensor Product Representations (TPRs; Smolensky (1990), Smolensky & Legendre (2006)). After an initial brief…
We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of…
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We present a variation of the proof in the first author's "Mob families and mad families" of Con(b<a), which in particular removes some of the obstacles to generalising the argument to uncountable cardinals.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
An elementary proof of an identity by Lyons, Paule and Riese is given. It is simpler than all the 3 published proofs.
In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the higher order integral polynomial case. However, they did not…
We show that the auxiliary variable method (M{\o}ller et al., 2006; Murray et al., 2006) for inference of Markov random fields can be viewed as an approximate Bayesian computation method for likelihood estimation.
We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate…