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Notes from the International Autumn School on Computational Number Theory

  • Book
  • © 2019

Overview

Editors:
  1. Ilker Inam

    1. Department of Mathematics, Faculty of Arts and Science, Bilecik Şeyh Edebali University, Bilecik, Turkey

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  2. Engin Büyükaşık

    1. Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey

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    You can also search for this editor in PubMed   Google Scholar

  • Presents lecture notes from the 2017 International Autumn School of Computational Number Theory
  • Offers graduate students a valuable introduction to computational number theory
  • Encourages future research by providing up-to-date knowledge from experts in the field

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Lecture Notes

    1. Front Matter

      Pages 1-1
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    2. An Introduction to Modular Forms

      • Henri Cohen
      Pages 3-62

    3. Computational Arithmetic of Modular Forms

      • Gabor Wiese
      Pages 63-170

    4. Computational Number Theory in Relation with L-Functions

      • Henri Cohen
      Pages 171-266

    5. Exponential Diophantine Equations

      • Florian Luca
      Pages 267-309

  3. Research Contributions

    1. Front Matter

      Pages 311-311
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    2. Nullstellensatz via Nonstandard Methods

      • Haydar Göral
      Pages 313-322

    3. 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

    4. On Higher Congruences Between Cusp Forms and Eisenstein Series. II.

      • Bartosz Naskręcki
      Pages 331-353

    5. Lucas Numbers Which are Products of Two Balancing Numbers

      • Zafer Şiar
      Pages 355-363
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Faculty of Arts and Science, Bilecik Şeyh Edebali University, Bilecik, Turkey

    Ilker Inam

  • Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey

    Engin Büyükaşık

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