Topic
Algebraic function
About: Algebraic function is a research topic. Over the lifetime, 2795 publications have been published within this topic receiving 60059 citations.
Papers published on a yearly basis
1 / 3
Papers
Book•
25 Jun 1993
TL;DR: This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material.
Abstract: The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.
2,480 citations
1 Jan 1973
2,371 citations
TL;DR: In this article, the irreducible representations of semisimple algebraic groups of characteristic p 0 were studied, in particular the rational representations, and all of the representations of corresponding finite simple groups.
Abstract: Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)
1,547 citations
TL;DR: In this article, the existence of a smooth control-Lyapunov function implies smooth stabilizability, and the result is extended to real-analytic and rational cases as well.
1,479 citations
TL;DR: In this paper, a one-dimensional Schrodinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices.
Abstract: A one-dimensional Schr\"odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices. When the potential is periodic, the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength. This critical index is also evaluated as the solution to an escape-rate problem for the recursion relations.
1,173 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 10 |
| 2023 | 21 |
| 2022 | 25 |
| 2021 | 49 |
| 2020 | 39 |