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Algebraic number

About: Algebraic number is a(n) research topic. Over the lifetime, 20611 publication(s) have been published within this topic receiving 315606 citation(s).

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Book
01 Jan 1960-
Abstract: © Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

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4,337 citations


Journal ArticleDOI

2,342 citations


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.

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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.

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1,906 citations


Book
01 Jan 1973-
Abstract: Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.

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1,762 citations


Journal ArticleDOI
K.G. Chetyrkin1, F.V. Tkachov1Institutions (1)
23 Nov 1981-Nuclear Physics
Abstract: The following statement is proved: the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic “algebraic” procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind. The number of steps is a rapidly increasing function of the complexity of the diagram. To demonstrate further possibilities offered by the technique we compute the 5-loop diagram contributing to the anomalous field dimension γ 2 ( g ) in the ϕ 4 model, that defied, heretofore, analytical calculation by other methods.

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1,639 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202220
2021914
20201,072
2019964
2018865
2017855

Top Attributes

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Topic's top 5 most impactful authors

Artūras Dubickas

35 papers, 274 citations

Ioannis Z. Emiris

28 papers, 699 citations

Yann Bugeaud

25 papers, 706 citations

Saugata Basu

20 papers, 1.8K citations

Jaume Llibre

19 papers, 584 citations