Related papers: D\'emonstration de l'Observation 2 d'Almkvist et Z…
In this note, we prove two supercongruences involving Almkvist--Zudilin sequences, which were originally conjectured by Z.-H. Sun.
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Ap\'{e}ry numbers, by means of a general…
A.E. Allahverdyan and Th. M. Nieuwenhuizen [1] in their paper "A mathematical theorem as a basis for the second law: Thomson's formulation applied to equilibriium" present a proof of the second law of thermodynamics based on quantum…
We provide a short proof of the intriguing characterisation of the convex order given by Wiesel and Zhang.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
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 present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We give a brief proof of a recent result of Avron, Seiler and Simon.
We present three proofs of an observation of Ahmadi on the number of irreducible polynomials over $\text{GF}(2)$ with certain traces and cotraces, the most interesting of which uses an explicit natural bijection. We also present two proofs…
The Lorentzian distance formula, conjectured several years ago by Parfionov and Zapatrin, has been recently proved by the second author. In this work we focus on the derivation of an equivalent expression in terms of the geometry of…
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxiv.org:math/0809.1635.
We give a short proof of Ahlfors' theorem on covering surfaces.
This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament's Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden.
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
We give a brief exposition of the 2d TQFT that captures the structure of the GL Verlinde numbers, following Witten.
We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
We give a very concise proof of Ornstein's $L^1$ non-inequality for first- and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported on three points.