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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.

(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, 133 (2013) 1372-1388.

(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.

Arithmetic from an advanced perspective: An introduction to the adeles, Pro Mathematica, 24 (2010) 9-54.

(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.

(with A. Pillai), On diophantine approximation along algebraic curves, Proceedings of the A.M.S.,136 (2008) 11-19.

A tail of two palindromes, The American Mathematical Monthly,112 (2005) 311-321.

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.

On Newton’s method and rational approximations to quadratic irrationals, Canadian Mathematical Bulletin, 47 (2004), 12-16.

(with A. Folsom, A. Pekker, R. Roengpitya, J. Snyder), On a quantitative refinement of the Lagrange spectrum, Acta Arithmetica,102 (2002), 55-82.

(as Drew Aderburg), “Math Forum”—I couldn’t keep my distance: A mathematical seduction, Math Horizons, February 2002, 12-15.

Diophantine inequalities and irrationality measures for certain transcendental numbers, Indian J. of Pure and Applied Math.,32 (2001), 1591-1599.

(with M. Starbird), From Play to Power: Bringing Infinity to Humanities Students, Math. Ed. Reform Forum,13 (2001) 1-5.

On a question of Mordell and a spectrum of linear forms, J. of the London Math. Society, 62 (2000) 701-715.

(with M. Starbird), Abandoning Dead Ends: Embracing Lively Beginnings, MAA Focus, 9 (2000) 10-11.

Diophantine Olympics and World Champions: Polynomials and primes down under, The American Mathematical Monthly,107 (2000) 822-829.

(with A.J. van der Poorten), On periods of elements from real quadratic number fields, Canadian Math. Soc. Conference Proceedings, 27 (2000) 35-43.

On simultaneous diophantine approximation in the vector space Q+Qa, Journal of Number Theory, 82 (2000) 12-24.

(with J.M. Todd), On diophantine approximation below the Lagrange constant, Fibonacci Quarterly, 38 (2000) 136-144.

(with M. Starbird), Pleasures vs. Problems, Notices of the American Mathematical Society, 47 February 2000.

On Real Quadratic Number Fields and Simultaneous Diophantine Approximation, Monatshefte Math.,128 (1999) 201-209.

Mathematics Beyond the Ivy-Covered Hall: Can we Read the Writing on the Wall?, The Mathematical Intelligencer, 20 (1998) 1-2.

(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.

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.

Uniformly approximable numbers and the uniform approximation spectrum, Journal of Number Theory, 61 (1996) 194-208.

(with C.S. Kollett), On the structure of quadratic irrationals associated with generalized Fibonacci and Lucas numbers, Fibonacci Quarterly, 34 (1996) 200-212.

On Liouville decompositions in local fields, Proceedings of the A.M.S.,124 (1996) 3305-3310.

(with T. Struppeck), Does Summation 1/n! really converge? Infinite series and p-adic analysis, The American Mathematical Monthly,103 (1996) 565-577.

(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.

Transcendence and irrationality measures, “Proceedings of the Seminar on the Theory of Numbers”, University of Caen, France, 1994 [not refereed].

Inhomogeneous inequalities over number fields, Illinois J. Math., 38 (1994) 452-470.

(with T. Struppeck), On frequency distributions of partial quotients of U-numbers, Mathematika,40 (1993) 215-225.

(with J.D. Vaaler), On the decomposition of vectors over number fields, J. reine angew. Math.,435 (1993) 197-219.

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.

On Mahler’s compound bodies, J. Austral. Math. Society (Series A), 55 (1993) 183-215.

Homogeneous Diophantine Approximation in S-integers, Pacific J. Math.,152 (1992) 211-253.