Zeta functions

December 1-5, 2008, Moscow, Russia




Practical details


Michel L. Lapidus
University of California Riverside, USA
lapidus (at) math.ucr.edu

Fractal Geometry and Number Theory: Zeta Functions and Complex Dimensions

In this talk, we will give an overview of aspects of the theory of complex fractal dimensions, geometric zeta functions, and fractal strings, as developed in the recent (joint) monograph [1] (and in a number of earlier and later research papers). If time permits, we will also discuss aspects of the theory developed in the author’s recent book [2], in which is proposed a new approach to the Riemann hypothesis, based in part on the moduli space of fractal membranes and the expected properties of the associated (but still conjectural) modular flow.

[1] M. L. Lapidus and M. van Frankenhuijsen, Fractal Geometry, Complex Dimensions and Zeta Functions (Geometry and spectra of fractal strings), Springer Monographs in Mathematics, Aug. 2006, approx. 500pp. (See also by the same authors: Fractal Geometry and Number Theory (Complex dimensions of fractal strings and zeros of zeta functions), Birkhauser, Boston, 2000, approx. 300pp.)
[2] M. L. Lapidus, In Search of the Riemann Zeros (Strings, fractal membranes and noncommutative spacetimes), Amer. Math. Soc., Providence, RI, Jan. 2008, approx. 600pp.

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