Related papers: Supercongruences for sporadic sequences
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We discuss and reinterpret a 4d conformal triality recently discovered in the literature in terms of ordinary Seiberg duality. We observe that a non-abelian global symmetry is explicitly realized by only two out of the three phase. We…
Let $p$ be an odd prime. In this paper, by using the well-known Karlsson-Minton summation formula, we mainly prove two supercongruences as variants of a supercongruence of Deines-Fuselier-Long-Swisher-Tu, which confirm some recent…
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with…
In this paper, we introduce and investigate a new notion of exact sequences of semimodules over semirings relative to the canonical image factorization. Several homological results are proved using the new notion of exactness including some…
We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomial coefficients $\binom{2k}{k}$.
Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.
In this note, we present a relationship between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…