9 research outputs found
Ternary codes associated with and power moments of Kloosterman sums with trace nonzero square arguments
In this paper, we construct two ternary linear codes
and , respectively associated with the orthogonal groups
and . Here is a power of three. Then we obtain two recursive formulas for the power moments of Kloosterman sums with "trace nonzero square arguments\u27\u27 in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups
Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
In this paper, we construct two binary linear codes associated with
multi-dimensional and m-multiple power Kloosterman sums (for any
fixed m) over the finite field Fq. Here q is a
power of two. The former codes are dual to a subcode of the binary
hyper-Kloosterman code. Then we obtain two recursive formulas for
the power moments of multi-dimensional Kloosterman sums and for the
m-multiple power moments of Kloosterman sums in terms of the
frequencies of weights in the respective codes. This is done via
Pless power moment identity and yields, in the case of power moments
of multi-dimensional Kloosterman sums, much simpler recursive
formulas than those associated with finite special linear groups
obtained previously
International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library
Number Theory, Analysis and Geometry: In Memory of Serge Lang
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future.
In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas, namely number theory, analysis and geometry, representing Lang’s own breadth of interests. A special introduction by John Tate includes a brief and engaging account of Serge Lang’s life
Number Theory, Analysis and Geometry: In Memory of Serge Lang
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future.
In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas, namely number theory, analysis and geometry, representing Lang’s own breadth of interests. A special introduction by John Tate includes a brief and engaging account of Serge Lang’s life