5 papers
Möbius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications
Max A. Alekseyev
A coefficient duality first encountered for formal Bernoulli series is shown to be equivalent to a general Möbius covariance law for formal power series. We obtain a structural cha…
Generalization of Ramanujan's formula for sums of half-integer powers of consecutive integers via formal Bernoulli series
Max A. Alekseyev, Rafael Gonzalez, Keryn Loor +2
Faulhaber's formula expresses the sum of the first positive integers, each raised to an integer power , as a polynomial in of degree . Ramanujan expressed thi…
Computing bounded solutions to linear Diophantine equations with the sum of divisors
Max A. Alekseyev
We propose an efficient computational method for finding all solutions to the Diophantine equation , where integer coefficient and an upper bound…
Classifying integral Grothendieck rings up to rank 5 and beyond
Max A. Alekseyev, Winfried Bruns, Jingcheng Dong +1
In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its fo…
On the -adic valuations of values of Legendre polynomials
Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also…