Bibliography

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.
Dynamical, Spectral and Arithmetic Zeta Functions

With Michel L. Lapidus, editors

Contemporary Mathematics 290, AMS, Providence, RI, 2001.
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.
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]

The ABC Conjecture implies Roth's Theorem and Mordell's Conjecture [PDF]
Matematica Contemporanea 16 (1999), 45-72.
A Lower Bound in the ABC Conjecture
J. Number Theory 82 (2000), 91-95.
The ABC conjecture implies Vojta's Height Inequality for Curves
J. Number Theory 95 (2002), 289-302
Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation [PDF]
With M. L. Lapidus

Experimental Mathematics 12 (2003), 41-69.
Arithmetic Progressions of Zeros of the Riemann Zeta Function [PDF]
J. Number Theory 115 (2005), 360-370.
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.
Phase transitions on Hecke C*-algebras and class-field theory over Q
With Marcelo Laca

J. reine angewandte Math. 595 (2006), 25-53.
ABC implies the Radicalized Vojta Height Inequality for Curves [PDF]
J. Number Theory 127 (2007), 292--300.
The Two-Variable Zeta Function and The Riemann Hypothesis for Function Fields [PDF]
Expositiones Mathematicae 26/3 (2008), 249--260.

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.
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.
Fractality, Self-Similarity and Complex Dimensions [PDF]
With M. L. Lapidus

In: Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

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