The Net Advance of Physics:
NUMBER THEORY

NUMBER THEORY:

• General: Archives: Algebraic Number Theory Preprint Archive;

• General: Homepages: Number Theory Web; Mathematical Atlas;

• General: Textbooks: Jia 96;
  • Elementare Zahlentheorie by Yauheniya Abramchuk et al. [2018/09] Number-theory textbook in German; 151 pp.

• General: Campbell's Glossary; Kim 2002/10;

• Type: COMPUTATIONAL:
  • Computational Number Theory in Relation with L-Functions by Henri Cohen [2018/09]

• Aspects: DIOPHANTINE EQUATIONS; SIEVES; ZETA FUNCTIONS;

• Aspects: ALGEBRAIC NUMBERS:
  • Notes on the Theory of Algebraic Numbers by Steve Wright [2015/07] Notes for a second-semester graduate course.

• Aspects: BASEL PROBLEM:
  • A One-Sentence and Truly Elementary Proof of the Basel Problem by Samuel G. Moreno [2015/02] with long list of references

• Aspects: CONTINUED FRACTIONS:
  • Continued Fractions by Alain Lasjaunias [2017/11]

• Aspects: CRYPTOGRAPHY:
  • Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography by N. Tokareva et al. [2017/10] Including some still-unsolved problems.
  • Review on DNA Cryptography by Mandrita Mondal and Kumar S. Ray [2019/04]

• Aspects: CYCLOTOMIC NUMBERS:
  • Jacobi Sums and Cyclotomic Numbers: A Survey Report by Md. Helal Ahmed and Jagmohan Tanti [2019/06]

• Aspects: GEOMETRY OF NUMBERS:
  • Mahler's Work on the Geometry of Numbers by Jan-Hendrik Evertse [2018/06]

• Aspects: GOLDEN RATIO:
  • Fibonacci numbers and the golden ratio by Robert Schneider [2016/11]

• Aspects: INTEGER SEQUENCES:
  • The On-Line Encyclopedia of Integer Sequences: A fingerprint file for mathematics by N. J. A. Sloane [2021/05]

• Aspects: JACOBI SUMS:
  • Jacobi Sums and Cyclotomic Numbers: A Survey Report by Md. Helal Ahmed and Jagmohan Tanti [2019/06]

• Aspects: LUCAS'S THEOREM:
  • Lucas' theorem: its generalizations, extensions and applications (1878--2014) by Romeo Meštrović [2014/09]

• Aspects: MODULAR FORMS:
  • An Introduction to Modular Forms by Henri Cohen [2018/09]

• Aspects: PRIMES:
  • The Green-Tao theorem: an exposition by David Conlon et al. [2014/03] (Prime numbers contain arbitrarily long arithmetic progressions.)
  • Gaps between Primes by James Maynard [2019/10]
  • The work of James Maynard by K. Soundararajan [2022/07] On prime numbers.
  • Rhymes in primes by A. Okounov [2022/07]

• Aspects: REALS:
  • The real numbers -- a survey of constructions by Ittay Weiss [2015/06]

• Aspects: RESIDUES:
  • Topics in the Theory of Quadratic Residues by Steve Wright [2014/08]

• Aspects: SALEM NUMBERS:
  • Salem numbers: a survey by Chris Smyth [2014/08]

• Aspects: STIRLING NUMBERS:
  • Close Encounters with the Stirling Numbers of the Second Kind by Khristo N. Boyadzhiev [Mathematics Magazine 85(4), 252 (2012)]

• Aspects: WEIL SUMS:
  • Weil sums of binomials: properties and applications by Daniel J. Katz [2018/05]

• Re: COMPLEXITY:
  • Interactions of Computational Complexity Theory and Mathematics by Avi Wigderson [2017/10]

• Re: L FUNCTIONS:
  • Computational Number Theory in Relation with L-Functions by Henri Cohen [2018/09]

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