Related papers: Multiplicity One Theorems, S-Version
We present an elliptic version of Selberg's integral formula.
We introduce the multivariable connected sum which is a generalization of Seki-Yamamoto's connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating…
The Multiverse is collection of parallel universes. In this article a formal theory and a topos-theoretic models of the multiverse are given. For this the Lawvere-Kock Synthetic Differential Geometry and topos models for smooth…
We show that there is a bijection between real-linear automorphisms of the multicomplex numbers of order $n$ and signed permutations of length $2^{n-1}$. This allows us to deduce a number of results on the multicomplex numbers, including a…
We give a purely combinatorial proof for a two-fold generalization of van der Waerden-Brauer's theorem and Hindman's theorem. We also give tower bounds for a finite version of it.
A very simple but useful almost sure convergence theorem of probability is given.
In this revised version, we add some expository material and references and make some minor corrections.
A parallel result of (the classical) Sledd--Stegenga's $H^1\rightarrow L^1$ multiplier theorem was obtained on the $H^1$ space under the anisotropic settings. Based on the same technique, an $H^1\rightarrow L^p$ multiplier theorem is also…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
We derive a symplectic analogue of A-directed immersion theorem.
We connect Dedekind sums and some formulas for numerical semigroups.
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations.…
We give an elementary proof to Hasse theorem.
In this note, we present a proof of Donaldson's Diagonalization Theorem via an abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple spinors. Like the other proof of Donaldson's theorem using the standard…
In this paper, we give corrected and improved definitions of the sets $S$ and $\Delta$ compared to [1]. By using these new definitions, we go throughout the proof of the main result in [1], and we correct it.
We give a new simpler proof of a theorem of Jayne and Rogers.
We show that for any prime prime $p\not=2$ $$\sum_{k=1}^{p-1} {(-1)^k\over k}{-{1\over 2} \choose k} \equiv -\sum_{k=1}^{(p-1)/2}{1\over k} \pmod{p^3}$$ by expressing the l.h.s. as a combination of alternating multiple harmonic sums.