The Warsaw period of Voronoï’s creative work. (English) Zbl 0952.01036
Engel, P. (ed.) et al., Voronoï’s impact on modern science. Book I. Transl. from the Ukrainian. Kyiv: Institute of Mathematics. Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 21(1), 29-33 (1998).
This paper gives a review of Voronoï’s work during the Warsaw period. This review concerns many aspects in mathematics:
Diophantine approximation: generalization of continued fraction algorithms.
Algebraic number theory: number of irreducible factors of a polynomial modulo a prime.
Analytic number theory: summation on the function “number of divisors of \(n\)” and application to study the number of integer points in a circle; summation on the function “number of representations of \(n\) by a positive definite quadratic form”.
Geometry of numbers: minima of positive quadratic forms.
Voronoï tessellations which have many applications outside mathematics.
For the entire collection see [Zbl 0928.00008].
Diophantine approximation: generalization of continued fraction algorithms.
Algebraic number theory: number of irreducible factors of a polynomial modulo a prime.
Analytic number theory: summation on the function “number of divisors of \(n\)” and application to study the number of integer points in a circle; summation on the function “number of representations of \(n\) by a positive definite quadratic form”.
Geometry of numbers: minima of positive quadratic forms.
Voronoï tessellations which have many applications outside mathematics.
For the entire collection see [Zbl 0928.00008].
Reviewer: Eugène Dubois
MSC:
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 11-03 | History of number theory |
| 11H06 | Lattices and convex bodies (number-theoretic aspects) |
| 11H55 | Quadratic forms (reduction theory, extreme forms, etc.) |
| 11H31 | Lattice packing and covering (number-theoretic aspects) |
| 05B45 | Combinatorial aspects of tessellation and tiling problems |
| 01A60 | History of mathematics in the 20th century |
