Related papers: A weighted version of Saitoh's conjecture
We give in this note a weighted version of Brianchon-Gram's decomposition for a simple polytope. This weighted version is a direct consequence of the ordinary Brianchon-Gram formula.
We give a more strong heuristic justification of our conjecture on the excess of the odious primes.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
We obtain another proof of Hermite's integral for the Hurwitz zeta function.
We prove the following conjecture of Leighton and Moitra. Let $T$ be a tournament on $[n]$ and $S_n$ the set of permutations of $[n]$. For an arc $uv$ of $T$, let $A_{uv}=\{\sigma \in S_n \, : \, \sigma(u)<\sigma(v) \}$. $\textbf{Theorem.}$…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
We introduce the notion of a weighted $\delta$-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted $\delta$-vectors from a combinatorial perspective. We present a version of Ehrhart…
We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
This is a survey on Sarnak's Conjecture
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
We prove the weight part of Serre's conjecture for Galois representations valued in $\mathrm{GSp}_4$ that are tamely ramified with explicit genericity at places above $p$ as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This…
We prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall's identity for the generalized hypergeometric function…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux;…
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.