
Gauss Hilbert • Research topics: approximation theory, numerical analysis, potential theory • My pearl idea is given in the 4th edition of the popular book "Proofs from the BOOK" (see "Pearl Lemma" on page 54). My paper about Hilbert's third problem is referenced on page 61. Pearls are called "basic points" in that paper (PDF), and are called pearls in a magazine article. • During 20122015 I will represent AMS at the Committee on American Mathematics Competitions. • Erdõs Number: 1.33 (that is, 2 with multiplicipy 3, 1+1/3=1.33) • Wiles Number in tennis: 2  this means that I played tennis with someone who played tennis with Andrew Wiles. • János Bolyai (see BolyaiLobachevsky geometry) may be a distant relative of mine. His mother was Zsuzsanna Árkosi Benkõ, and my father Pal Benko (a former world chess champion candidate) is coming from the Árkosi Benkõ family. Publications:
16.) (with P. D. Dragnev and V. Totik) Convexity of harmonic densities, Revista Mat. Iberoam. (to appear)
15.) (with P. D. Dragnev) Balayage pingpong: a convexity of equilibrium measures, Constr. Approx. 36 (2012), no. 2, 191–214.
14.) The Basel problem as a telescoping series, College Math. J. 43 (2012), no. 3, 244–250.
13.) (with S. B. Damelin and P. D. Dragnev) On supports of equilibrium measures with concave signed equilibria, J. Comput. Anal. Appl. 14 (2012), no. 4, 752–766.
12.) Weighted polynomial approximation for weak convex external fields, J. Math. Anal. Appl. 385 (2012), no. 1, 447–457.
11.) (with C. Ernst and D. Lanphier) Asymptotic bounds on the integrity of graphs and separator theorems for graphs. SIAM J. Discrete Math. 23 (2008/09), no. 1, 265–277  PDF
10.) (with A. Kroó) A Weierstrasstype theorem for homogeneous polynomials, Trans. Amer. Math. Soc., 361 (2009), 16451665  PDF
9.) (with D. Biles, M. P. Robinson, J. Spraker) Numerical Approximation for Singular Second Order Differential Equations (2009), Mathematical and Computer Modelling, 49, 11091114  PDF
8.) (with D. Biles, M. P. Robinson, J. Spraker) Nyström methods and singular secondorder differential equations, Comput. Math. Appl. 56 (2008), no. 8, 1975–1980.  PDF
7.) A new approach to Hilbert's third problem, Amer. Math. Monthly 114 (2007), no. 8, 665676  PDF
6.) (with S. B. Damelin and P. D. Dragnev) On the support of the equilibrium measure for arcs of the unit circle and for real intervals, Electron. Trans. Numer. Anal. 25 (2006), 2740  PDF
5.) The support of the equilibrium measure, Acta Sci. Math. (Szeged) 70 (2004), no. 12, 3555  PDF
4.) (with T. Erdélyi, and J. Szabados) The full MarkovNewman inequality for Müntz polynomials on positive intervals, Proc. Amer. Math. Soc. 131 (2003), no. 8, 23852391  PDF
3.) (with T. Erdélyi) Markov inequality for polynomials of degree n with m distinct zeros, J. Approx. Theory 122 (2003), no. 2, 241248  PDF
2.) Approximation by weighted polynomials, J. Approx. Theory 120 (2003), no. 1, 153182  PDF
1.) (with V. Totik) Sets with interior extremal points for the Markoff inequality, J. Approx. Theory 110 (2001), no. 2, 261265  PDF
Other works:
The Riemann zeta function and the striped anaconda, Polygon (to appear)
Get rich slowly, almost surely, The Mathematical Gazette (to appear)
A lotterylike stock market, Math Horizons, (2011 Febr.) 2428
The equilibrium measure and the Saff conjecture, Ph.D. dissertation (2006),
Approximation by weighted polynomials, Ph.D. dissertation (2001),
On Slowly Diverging Series, Polygon (1995), V.2, 89100
On the Number of Legal Chess Positions, Alpha (1995), no.1, 1011
Fast decreasing polynomials, Master thesis (1995), University of Szeged
On the generalization of the Fundamental Theorem of Algebra,
University of Szeged,
On Slowly Converging Series, Polygon (1994), IV.2, 95108
Collaborators: • D. Biles • S. Damelin • P. Dragnev • T. Erdélyi • C. Ernst • A. Kroó • D. Lanphier • M. Robinson • J. Spraker • J. Szabados • V. Totik
Problems: I have some challenging math problems which have been used in math contests. For example: (a) The following problem of mine was one of the problems at the prestigious Schweitzer competition. (This is an annual math competition in Hungary. Students get 1012 hard problems to solve; they can take them home and they have 10 days for thinking. They can even use the library.) Let C denote the set of all convergent series with strictly positive terms. Let D denote the set of all divergent series with strictly positive terms. Does a bijection between C and D exist which satisfies the following property? : If a_{n} and b_{n} are two elements of C and A_{n} and B_{n} are the corresponding elements in D, then a_{n} / b_{n} tends to zero if and only if A_{n} / B_{n} tends to infinity. (b) The following was given in the KÖMAL mathematics journal in the hardest problems category: Does a three variable real polynomial P(x,y,z) exist such that P(x,y,z) is positive if and only if we can construct a triangle from three line segments whose lengths are x, y and z?
