Complex dimensions of self-similar fractal strings and Diophantine approximation.
The Feynman integral and Feynman's operational calculus: a heuristic and mathematical introduction
Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function
We survey some of the universality properties of the Riemann zeta function and then explain how to obtain a natural quantization of Voronin’s universality theorem (and of its various extensions). Our work builds on the theory of complex fractal dimensions for fractal strings developed by the second author and M. van Frankenhuijsen in [60]. It also makes an essential use of the functional analytic framework developed by the authors in [25] for rigorously studying the spectral operator (mapping...
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