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President Burger - Journal Publications

President Burger’s research interests are in analytic number theory. In particular, he studies Diophantine analysis, the geometry of numbers, the theory of continued fractions, and how these issues connect to algebraic number theory. Here are the articles he has published in professional journals.

  1. Homogeneous Diophantine Approximation in S-integers, Pacific J. Math., 152 (1992) 211-253.
  2. On Mahler’s compound bodies, J. Austral. Math. Society (Series A), 55 (1993) 183-215.
  3. Badly approximable systems and inhomogeneous approximation over number fields, “Number Theory with an Emphasis on the Markoff Spectrum”, A. Pollington and W. Moran, eds., New York, Marcel Dekker, 1993.
  4. (with J.D. Vaaler), On the decomposition of vectors over number fields, J. reine angew. Math., 435 (1993) 197-219.
  5. (with T. Struppeck), On frequency distributions of partial quotients of U-numbers, Mathematika, 40 (1993) 215-225.
  6. Inhomogeneous inequalities over number fields, Illinois J. Math., 38 (1994) 452-470.
  7. Transcendence and irrationality measures, “Proceedings of the Seminar on the Theory of Numbers”, University of Caen, France, 1994 [not refereed].
  8. (with E. Dubois), Sur les quotients partiels de U-nombres dans un corps de series formelles, Comptes Rendus de l’Acedemie des Sciences ParisSerie I (1994) 421-426.
  9. (with T. Struppeck), Does Summation 1/n! really converge? Infinite series and p-adic analysis, The American Mathematical Monthly, 103 (1996) 565-577.
  10. On Liouville decompositions in local fields, Proceedings of the A.M.S., 124 (1996) 3305-3310.
  11. (with C.S. Kollett), On the structure of quadratic irrationals associated with generalized Fibonacci and Lucas numbers, Fibonacci Quarterly, 34 (1996) 200-212.
  12. Uniformly approximable numbers and the uniform approximation spectrum, Journal of Number Theory, 61 (1996) 194-208.
  13. Small solutions to systems of linear congruences over number fields, Rocky Mountain J. of Math.,Special volume in honor of W.M. Schmidt’s 60th birthday, 26 (1996) 875-888.
  14. (with F. Morgan), Fermat’s Last Theorem, the Four Color Conjecture, and Bill Clinton for April Fools’ Day, The American Mathematical Monthly, 104 (1997) 246-255.
  15. Mathematics Beyond the Ivy-Covered Hall: Can we Read the Writing on the Wall?, The Mathematical Intelligencer, 20 (1998) 1-2.
  16. On Real Quadratic Number Fields and Simultaneous Diophantine Approximation, Monatshefte Math., 128 (1999) 201-209.
  17. (with M. Starbird), Pleasures vs. Problems, Notices of the American Mathematical Society, 47 February 2000.
  18. (with J.M. Todd), On diophantine approximation below the Lagrange constant, Fibonacci Quarterly, 38 (2000) 136-144.
  19. On simultaneous diophantine approximation in the vector space Q+Qa, Journal of Number Theory, 82 (2000) 12-24.
  20. (with A.J. van der Poorten), On periods of elements from real quadratic number fields, Canadian Math. Soc. Conference Proceedings, 27 (2000) 35-43.
  21. Diophantine Olympics and World Champions: Polynomials and primes down under, The American Mathematical Monthly, 107 (2000) 822-829.
  22. (with M. Starbird), Abandoning Dead Ends: Embracing Lively Beginnings, MAA Focus, 9 (2000) 10-11.
  23. On a question of Mordell and a spectrum of linear forms, J. of the London Math. Society, 62 (2000) 701-715.
  24. (with M. Starbird), From Play to Power: Bringing Infinity to Humanities Students, Math. Ed. Reform Forum, 13 (2001) 1-5.
  25. Diophantine inequalities and irrationality measures for certain transcendental numbers, Indian J. of Pure and Applied Math., 32 (2001), 1591-1599.
  26. (as Drew Aderburg), “Math Forum”—I couldn’t keep my distance: A mathematical seduction, Math Horizons, February 2002, 12-15.
  27. (with A. Folsom, A. Pekker, R. Roengpitya, J. Snyder), On a quantitative refinement of the Lagrange spectrum, Acta Arithmetica, 102 (2002), 55-82.
  28. On Newton’s method and rational approximations to quadratic irrationals, Canadian Mathematical Bulletin, 47 (2004), 12-16.
  29. On sharp diophantine inequalities having only finitely many solutions, Proceedings on Analytic Number Theory and Surrounding Areas, Research Institute of Mathematical Sciences, Kyoto, Japan, 1384 (2004), 57-63.
  30. A tail of two palindromes, The American Mathematical Monthly, 112 (2005) 311-321.
  31. (with A. Pillai), On diophantine approximation along algebraic curves, Proceedings of the A.M.S., 136 (2008) 11-19.
  32. (with J. Gell-Redman, R. Kravitz, D. Walton, N. Yates), Shrinking the period lengths of continued fractions while still capturing convergents, Journal of Number Theory, 128 (2008) 144-153.
  33. Arithmetic from an advanced perspective: An introduction to the adeles, Pro Mathematica, 24 (2010) 9-54.
  34. (with D.C. Clyde, C.H. Colbert, G.H. Shin, Z. Wang), A Generalization of a Theorem of Lekkerkerker to Ostrowski’s Decomposition of Natural Numbers, Acta Arithmetica, 153 (2012) 217-249.
  35. (with D.C. Clyde, C.H. Colbert, G.H. Shin, Z. Wang), Canonical diophantine representations of natural numbers with respect to quadratic “bases”, Journal of Number Theory, (to appear) 18 pp.