Notes from the International Autumn School on Computational Number Theory

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

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.

• Galois representations
• modular forms
• Diophantine equations
• Number theory
• Nonstandard methods

• 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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