The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit form...The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.展开更多
The human mind understands logical processes and causality and formulates theories based on logical descriptions of empirical evidence. The Principles of Causal Conspiracy is based on defining information as logical c...The human mind understands logical processes and causality and formulates theories based on logical descriptions of empirical evidence. The Principles of Causal Conspiracy is based on defining information as logical charges similar to electric charges. Such information charges can be modeled in the vacuum of a quantum probability firmament as symmetry of quantum charges with a zero net charge. Observation of a state lifts one of these charges in a Möbius transformation from a multipolar field of possibilities that maximizes a local monopole field that is observable. In the first of several papers, I introduce new and profound principles, the Principles of Causal Conspiracy, to provide a consistent epistemology for quantum theory, relativity theory and all the known sciences.展开更多
Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tow...Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tower and its properties are applied as an approach to an indication that the Riemann hypothesis might be true. It is known that complex valued Power towers converge under certain conditions to exponential power towers of entire functions. These properties can be used to resolve the Riemann Hypothesis.展开更多
文摘The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.
文摘The human mind understands logical processes and causality and formulates theories based on logical descriptions of empirical evidence. The Principles of Causal Conspiracy is based on defining information as logical charges similar to electric charges. Such information charges can be modeled in the vacuum of a quantum probability firmament as symmetry of quantum charges with a zero net charge. Observation of a state lifts one of these charges in a Möbius transformation from a multipolar field of possibilities that maximizes a local monopole field that is observable. In the first of several papers, I introduce new and profound principles, the Principles of Causal Conspiracy, to provide a consistent epistemology for quantum theory, relativity theory and all the known sciences.
文摘Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tower and its properties are applied as an approach to an indication that the Riemann hypothesis might be true. It is known that complex valued Power towers converge under certain conditions to exponential power towers of entire functions. These properties can be used to resolve the Riemann Hypothesis.
