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Gert Almkvist

Publications and source records attributed to Gert Almkvist.

At least 19 recordsLinked to original sources
arXiv2021

Calabi-Yau operators of degree two

We show that the solutions to the equations defining the so-called Calabi-Yau condition for fourth order operators of degree two defines a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth order Calabi-Yau operators of degree two that are presently known to us.

math.AG↗
arXiv2014

More remarkable sinc integrals and sums

We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum version of Siegel-type lower bound. (cf. [2], Theorem 3)

math.CA↗
arXiv2013

About a class of Calabi-Yau differential equations

We explain an experimental method to find CY-type differential equations of order $3$ related to modular functions of genus zero. We introduce a similar class of Calabi-Yau differential equations of order $5$, show several examples and make a conjecture related to some geometric invariants. We finish the paper with a few examples of seven order.

math.NT↗
arXiv2012

Ramanujan-Sato-like series

Using the theory of Calabi-Yau differential equations we obtain all the parameters of Ramanujan-Sato-like series for $1/π^2$ as $q$-functions valid in the complex plane. Then we use these q-functions together with a conjecture to find new examples of series of non-hypergeometric type. To motivate our theory we begin with the simpler case of Ramanujan-Sato series for $1/π$.

math.NT↗
arXiv2011

Proof of some conjectured formulas for 1/pi by Z.-W. Sun

Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in [6] are simple transformations of known formulas for 1/pi.

math.NT↗
arXiv2010

Tables of Calabi--Yau equations

The main part of this paper is a big table containing what we believe to be a complete list of all fourth order equations of Calabi--Yau type known so far. In the text preceding the tables we explain what a differential equation of Calabi--Yau type is and we briefly discuss how we found these equations. We also describe an electronic version of this list.

math.AG↗
arXiv2008

Apery, Bessel, Calabi-Yau and Verrill

A differential equation related to the moments of Bessel functions is shown to have a solution at infinity with coefficients being squares of binomial coefficients.

math.CA↗
arXiv2007

Binomial identities related to Calabi-Yau differential equations

When searching for Calabi.Yau differential equations, often different formulas for the coefficients give the same differential equation. The coefficients are usually sums (simple, double or triple) of products of binomial coefficients. This results in numerous binomial identities.

math.CO↗
arXiv2006

Integrity of ghosts

Sequences of traces of powers of integral matrices are characterized.The result can be used can be used in character tables of e.g. the symmetric group.

math.CO↗
arXiv2006

Asymptotics of various partitions

Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.

math.NT↗