Related papers: Multiplicity One Theorems, S-Version
We prove a unified convergence theorem, which presents in four equivalent forms of the famous Antosik-Mikusinski Theorems. In particular, we show that Swartz' three uniform convergence principles are all equivalent to the Antosik-Mikusinski…
We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.
New version, including a variant of Quillen's proof of the Solomon-Tits theorem.
We sketch several proofs of F\'ary--Milnor theorem.
In this paper, we prove certain theorems about three consecutive primes.
We prove several extensions of the Erdos-Fuchs theorem.
In this work we show how the Multiplicity Polar Theorem can be used to calculate Chern numbers for a collection of 1-forms.
We prove Simon's conjecture for 3-manifolds.
We prove existence and multiplicity of symmetric solutions for the \emph{Schr\"odinger-Newton system} in three dimensional space using equivariant Morse theory.
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of…
We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a…
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We present several Orientifolds of M-Theory on $K_3\times S^1$ by additional projections with respect to the finite abelian automorphism groups of $K_3$. The resulting models correspond to anomaly free theories in six dimensions. We…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.
In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois…
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…