Notes from the International Autumn School on Computational Number Theory

Ilker Inam, Engin Büyükaşık (Herausgeber)

Buch | Softcover

XI, 363 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-12557-8 (ISBN)

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This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include:

Modular forms
L-functions
The modular symbols algorithm
Diophantine equations
Nullstellensatz
Eisenstein series

Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field aswell.

Part I: Lecture Notes.- An Introduction to Modular Forms.- Computational Arithmetic of Modular Forms.- Computational Number Theory in Relation with L-functions.- Exponential Diophantine Equations.- Part II: Research Contributions.- Nullstellensatz via Nonstandard Methods.- On the (1 + u2 + u3)-Constacyclic and cyclic codes over the finite ring F2 + uF2 + u2F2 + u3F2 + vF2.- On higher congruences between cusp forms and Eisenstein series.- Lucas Numbers which are Products of Two Balancing Numbers.

Erscheinungsdatum	04.05.2019
Reihe/Serie	Tutorials, Schools, and Workshops in the Mathematical Sciences
Zusatzinfo	XI, 363 p. 16 illus., 2 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	575 g
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	diophantine equations • Galois representations • Modular Forms • Nonstandard methods • Number Theory
ISBN-10	3-030-12557-2 / 3030125572
ISBN-13	978-3-030-12557-8 / 9783030125578
Zustand	Neuware