Bibliography

Books

  1. Fractal Geometry and Number Theory (complex dimensions of fractal strings and zeros of zeta functions)
    With Michel L. Lapidus
    Birkhaeuser, 2000, 280 pages, ISBN 0-8176-4098-3.
  2. Dynamical, Spectral and Arithmetic Zeta Functions
    With Michel L. Lapidus, editors
    Contemporary Mathematics 290, AMS, Providence, RI, 2001.
  3. Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot
    With Michel L. Lapidus, editors
    Proceeding of Symposia in Pure Mathematics 72, Part 1 and 2, AMS, Providence, RI, 2004.
  4. Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings
    With Michel L. Lapidus
    Springer Monographs in Mathematics, 2006, 480 pages, ISBN 0387332855.
    Errata and corrected pages [ps]

Papers

  1. The ABC Conjecture implies Roth's Theorem and Mordell's Conjecture [PDF]
    Matematica Contemporanea 16 (1999), 45-72.
  2. A Lower Bound in the ABC Conjecture
    J. Number Theory 82 (2000), 91-95.
  3. The ABC conjecture implies Vojta's Height Inequality for Curves
    J. Number Theory 95 (2002), 289-302
  4. Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation [PDF]
    With M. L. Lapidus
    Experimental Mathematics 12 (2003), 41-69.
  5. Arithmetic Progressions of Zeros of the Riemann Zeta Function [PDF]
    J. Number Theory 115 (2005), 360-370.
  6. Phase transitions on Hecke C*-algebras and class-field theory
    With Marcelo Laca
    In: Noncommutative Geometry and Number Theory (Marcolli and Consani, eds.), Aspects of Mathematics E 37, Vieweg, 2006.
  7. Phase transitions on Hecke C*-algebras and class-field theory over Q
    With Marcelo Laca
    J. reine angewandte Math. 595 (2006), 25-53.
  8. ABC implies the Radicalized Vojta Height Inequality for Curves [PDF]
    J. Number Theory 127 (2007), 292--300.
  9. The Two-Variable Zeta Function and The Riemann Hypothesis for Function Fields [PDF]
    Expositiones Mathematicae 26/3 (2008), 249--260.

Conference Proceedings

  1. Complex dimensions of fractal strings and oscillatory phenomena in fractal geometry and arithmetic
    With M. L. Lapidus
    In: Spectral problems in geometry and arithmetic (T. Branson, ed.), Contemp. Math. 237, AMS, Providence, RI, 1999, pp. 87-106.
  2. A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation [PDF]
    With M. L. Lapidus
    In: Dynamical, Spectral and Arithmetic Zeta Functions, Contemp. Math. 290, AMS, Providence, RI, 2001, pp. 113-138.
  3. Fractality, Self-Similarity and Complex Dimensions [PDF]
    With M. L. Lapidus
    In: Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Chapters

  1. The Riemann Hypothesis for Function Fields over a Finite Field [PDF]
    for Nova Science Publishers, arXiv:0806.0044v2 [math.NT].

Preprints

  1. The abc theorem for meromorphic functions [PDF]
    arXiv:0805.1729v1 [math.NT]