In Search of the Riemann Zeros: Strings, Fractal Membranes and Noncommutative SpacetimesAmerican Mathematical Soc., 2008 - 558 sider Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line. |
Indhold
Introduction | 1 |
String Theory on a Circle and TDuality Analogy with the Riemann Zeta Function | 21 |
Fractal Strings and Fractal Membranes | 89 |
Noncommutative Models of Fractal Strings Fractal Membranes and Beyond | 155 |
Towards an Arithmetic Site Moduli Spaces Fractal Strings and Membranes | 197 |
Vertex Algebras | 315 |
The Weil Conjectures and the Riemann Hypothesis | 325 |
The Poisson Summation Formula with Applications | 347 |
The Selberg Class of Zeta Functions | 389 |
The Noncommutative Space of Penrose Tilings and Quasicrystals | 411 |
| 453 | |
Conventions | 491 |
| 503 | |
| 551 | |
Almindelige termer og sætninger
algebra analogy Appendix arithmetic arithmetic geometries associated automorphic called Chapter classical closed commutative complex complex dimensions Conjecture connected consider construction context continuous corresponding counterpart defined definition denotes discussion dynamical earlier elements equal equation equivalently especially example extended fact factor field finite flow formula fractal membranes fractal strings functional equation further Furthermore geometry given hence infinite integers interested interpretation introduced latter lattice length manifold mathematical measure metric moduli space Moreover multiplicative natural noncommutative notation notion obtained operator particular partition function physical poles positive precisely present prime Problem proof properties quantum quantum mechanics reader Recall references Remark resp respectively Ricci Riemann Hypothesis satisfies Section self-similar sense sequence spectral standard string theory suitable Theorem tilings topology vertex viewed zeros zeta function
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