Remainder estimates for Levin-type sequence transformations are discussed. A new remainder estimate is introduced which is related to the Kummer transformation. Test cases are presented which show that the new remainder estimate can enhance the performance of Levin-type sequence transformations considerably.

Christiane Kummer, Die Illustration der Würzburger Bischofschronik des Lorenz Fries aus dem Jahre 1546. Ein Hauptwerk Martin Segers und seiner Werkstatt (Veröffentlichungen Stadtarchivs Würzburg, Bd. 7), Würzburg (Ferdinand Schöningh) 1995, 354 S., 32 Abb.

By making use of the linearization method, we examine a class nonterminating 3F2-series with five free integer parameters that yields twenty summation formulae. Under Kummer and Thomae transformations, six classes exotic are consequently evaluated in closed forms. There overall 100 identities recorded present paper

In this note, we calculate the boundary of movable cones and nef generalized Kummer 4-fold $\mathrm{Km}^2(A)$ attached to an abelian surface $A$ with $\mathrm{rk} \mathrm{NS}(A) = 1$.

Kida, Rikuna and Sato [6] developed a classification theory for Brumer’s quintic polynomials via Kummer arising from associated elliptic curves. We generalize their results to curves Lecacheux’s $F_{20}$-polynomials instead of $D_{5}$-polynomials.

There are two types of numerically trivial involutions of an Enriques surface according as their period lattice. One is U(2) ⊥ U(2)-type and the other is U ⊥ U(2)-type. An Enriques surface with an involution of U(2) ⊥ U(2)-type is doubly covered by a Kummer surface of product type, and such involutions are classified again into two types according as the parity of the corresponding Göpel subgro...

This paper introduces high-security constant-time variable-base-point Diffie–Hellman software using just 274593 Cortex-A8 cycles, 91460 Sandy Bridge cycles, 90896 Ivy Bridge cycles, or 72220 Haswell cycles. The only higher speed appearing in the literature for any of these platforms is a claim of 60000 Haswell cycles for unpublished software performing arithmetic on a binary elliptic curve. The...

We complete the classification of order $5$ nonsymplectic automorphisms on hyper-Kahler fourfolds deformation equivalent to Hilbert square a K3 surface. then compute topological Lefschetz number natural generalized Kummer and we describe geometry their fix loci.

In this article we investigate the Bernoulli numbers B̂n associated to the formal group laws whose canonical invariant differentials generate the Lucas sequences {Un} and {Vn}. We give explicit expressions for these numbers and prove analogues of Kummer congruences for them.

and Applied Analysis 3 Remark 1. (a) In (12) and (13), if we set d = 2a, we recover (5) and (6), respectively. (b) Using (12) and (13), Kim et al. [12] have obtained the following extension of transformation (7) due to Kummer: