Notes from the International Autumn School on Computational Number Theory (Tutorials, Schools, and Workshops in the Mathematical Sciences)

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 as well. "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 as well."-- Back cover Front Matter ....Pages i-xi Front Matter ....Pages 1-1 An Introduction to Modular Forms (Henri Cohen)....Pages 3-62 Computational Arithmetic of Modular Forms (Gabor Wiese)....Pages 63-170 Computational Number Theory in Relation with L-Functions (Henri Cohen)....Pages 171-266 Exponential Diophantine Equations (Florian Luca)....Pages 267-309 Front Matter ....Pages 311-311 Nullstellensatz via Nonstandard Methods (Haydar Göral)....Pages 313-322 On the \((1+u^2+u^3)\)-Constacyclic and Cyclic Codes Over the Finite Ring \( {F}_2+u{F}_2+u^2{F}_2+u^3{F}_2+v{F}_2 \) (G. Gözde Güzel, Abdullah Dertli, Yasemin Çengellenmiş)....Pages 323-329 On Higher Congruences Between Cusp Forms and Eisenstein Series. II. (Bartosz Naskręcki)....Pages 331-353 Lucas Numbers Which are Products of Two Balancing Numbers (Zafer Şiar)....Pages 355-363