RESEARCH

    My mathematical interests live mostly in areas of number theory including small gaps between primes, algebraic number theory, Iwasawa theory, transcendence/irrationality, elliptic curves, continued fractions, and modular forms. Additionally, I am interested in combinatorics, group actions, and the mathematical content of music, art, and social justice. 

    Research Articles:

• 1. Keith Billington, Maddie Cheng, Jordan Schetter, and Ade Irma Suriajaya, The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function, submitted, in review

  2. Daniel Goldston, Apoorva Panidapu, and Jordan Schettler, Explicit Calculations for Sono's Multidimensional Sieve of E_2-Numbers, Mathematics of Computation, (2024), DOI: https://doi.org/10.1090/mcom/3938

  3. Daniel Goldston, Apoorva Panidapu, and Jordan Schettler, Small Gaps Between Three Almost Primes and Almost Prime Powers, Acta Arithmetica, 203 (2022), 1-18, DOI: 10.4064/aa210325-27-11

  4. Ethan Berkove and Jordan Schettler, The Hypercube Corner Poset with an Application to an n-Dimensional Cube Stacking Puzzle,  Australasian Journal of Combinatorics, 84 (2022), 86-110, ISSN: 2202-3518

  5. Emily Henderson and Jordan Schettler, How to Tune a Stiff Sawtooth, Bridges Conference Proceedings, (2022), 363-366

  6. Jordan Schettler, Dalibraic Topology, Journal of Mathematics and the Arts, 15 (2021), 137-149, DOI 10.1080/17513472.2021.1940468

  7. Daniel Goldston, Sidney Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, and Cem Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II, Journal of Number Theory, 221 (2020), 222-231, DOI 10.1016/j.jnt.2020.06.002

  8. Wes Maciejewski, John Bragelman, Marion Campisi, Tim Hsu, Andrea Gottlieb, Jordan Schettler, Trisha Bergthold and Bem Cayco, Change Comes from Without: Lessons Learned in a Chaotic Year, Problems, Resources, and Issues in Mathematics Undergraduate Studies, (2020), DOI 10.1080/10511970.2020.1793854

  9. Mitchell Chavarria and Jordan Schettler, The Secret behind the Squiggles: Guitars with Optimally Curved Frets, Bridges Conference Proceedings, (2019), 279-286

  10. Jordan Schettler, Wendy Carlos’s Xenharmonic Keyboard, Mathematics Magazine, 92 (2019), no. 3, 201-212, DOI 10.1080/0025570X.2019.1569938

  11. Nicolas Brody and Jordan Schettler, Rational hyperbolic triangles and a quartic model of elliptic curves, Journal of Number Theory, 164 (2016), 359-374, DOI 10.1016/j.jnt.2016.01.004

  12. Jordan Schettler, Using Continued Fractions to Compute Iwasawa Invariants of Imaginary Quadratic Number Fields, Journal of Numbers, vol. 2014 (2014), 10 pages, DOI 10.1155/2014/803649

  13. Jordan Schettler, An Alternative Approach to Kida and Ferrero's Computations of Iwasawa λ-Invariants, Journal of Number Theory, 138 (2014), 84-96, DOI 10.1016/j.jnt.2013.11.014

  14. Jordan Schettler, Generalizations of Iwasawa's Riemann-Hurwitz Formula for Cyclic p-Extensions of Number Fields, International Journal of Number Theory, 10 (2014), 219-233, DOI 10.1142/S1793042113500905

  15. Jordan Schettler, The Change in Lambda Invariants for Cyclic p-Extensions of Zp-Fields, PhD Thesis, University of Arizona, ProQuest Dissertation Publishing, May 2012

  16. Lehmer's Totient Problem and Carmichael Numbers in a PID, Undergraduate Senior Thesis

    Expository Papers:

• 1. The Kummer Congruences, Divergent Series, and Nonstandard Analysis, pdf

  2. A p-adic Interpolative Property of Iwasawa Lambda Invariants, pdf

  3. Hilbert Functions, pdf

  4. The Lower Algebraic K-Groups, pdf

  5. Sheaf Cohomology, pdf

  6. Bernoulli Numbers, pdf

  7. Quadratic Reciprocity, pdf

  8. Periodic Continued Fractions, pdf

    Slides and Posters:

• 1. Class Numbers, Continued Fractions, and the Hilbert Modular Group, pdf

  2. A Brief Biography of Paul Erdős, pdf

  3. Ramanujan’s Continued Fractions and the Icosahedron, website

  4. Theory of Classical Modular Forms and Symbols, pdf

  5. An Introduction to Iwasawa Theory, pdf

  6. The Role of Continued Fractions in Rediscovering a Xenharmonic Tuning, pdf and aux files

  7. Zeta Zeros and Quantum Energy Levels, pdf

  8. Number Theoretic Analogs of The Riemann-Hurwitz Formula, pdf

  9. Cyclic p-Extensions of Zp-Fields, pdf

  10. (Special) Riemann-Hurwitz Formulas in Iwasawa Theory, pdf

  11. Slumdog Millionaire: Srinivasa Ramanujan, pdf

  12. Elliptic Curves Over Q, pdf

  13. The Brumer-Stark Conjecture, scanned notes

  14. Dynamics Over Number Fields, pdf

  15. Iwasawa Theory of Elliptic Curves and BSD in Rank Zero, pdf

  16. A Riemann-Hurwitz Formula for Number Fields, pdf

  17. Brauer's Theorems and the Meromorphicity of L-functions, pdf

  18. Voting Systems, Mass Murder, and the Enigma Machine, pdf

  19. Making Math Count in the Community: Measuring Income Disparity, ppt

  20. Smooth Manifolds and Minkowski Spacetime, pdf

  21. Deriving Meaning: Math at Work in RHS, pdf

  22. Base 18, Quaternions, Markov Chains, and Absurdity, pdf

  23. Hyperbolic Geometry, Complex Periods, Stereoscopy, and 4D, pdf

  24. How to Mathematize the World: Black Holes, Oil Spills, the Spread of AIDS, ..., pdf

  25. A Discrete Nash Demand Game with Diagonal Punishment, pdf