It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line. I make several assumptions and show that all zeros are on the critical line and that Riemann's functional equation presents a problem. The assumptions are, first, that Riemann's zeta function is single valued at each point of the critical strip (it is not), second, Riemann's functional equation necessarily and sufficiently sets zeroes in the critical strip (it does not) a...

The right to petition is more important than the right to vote. However, Federal judges violate civil rights by deciding cases (petitions) 1) cert denied without opinions, 2) with unpublished opinions, and 3) juries no longer are sole arbiters of law.

Public interest or case jurisdiction?- In deciding patent cases, Supreme Court holds both ways: Patent invalidity decision without looking at patent infringement claim or patent infringement claim decision Before Patent Invalidity defense

Petition for Certiorari Denied Without Opinion – Patent Case 98-1151.Patent Ownership and Assignment-Conflict of Federal and State Decisions-35 USC 261

In the past, we have had many metaphysical astronomical theories. Today, Hubble's law is the mainstay of modern theories which reasonably explains the Observed Universe. Some theories attempt to explain phenomena of observational astronomy alleged beyond the Observed Universe summarized in Hubble's law. Modern physical cosmology is dominated by the Big Bang metaphysical theory, which attempts to bring together observational astronomy and particle physics. Many questions of astronomy turn o...

By rearranging terms, Riemann's zeta function ζ(s) can be made to converge or diverge to any value desired. Accordingly, Riemann's analytic extension to interval 0≤x≤1 is irrelevant to determining primes.

Kepler published in 1609 his empirical laws of planetary motions about the Sun. Kepler's first law says that each planet (or comet) moves on a conic with the Sun as its focus. Newton published in 1687 solutions, called orbits, which have each object moving in a circle, ellipse, parabola or hyperbola thus expanding Kepler's observations. In Newton's solutions two bodies move on two separate conics. These conics each with a focus, orbit about the center of mass (barycenter) of the two bodies...

While extended zeta functions support investigations of Riemann's hypothesis and estimates for the Prime Number Theorem, some zeta functions offer better prospects for providing easy proofs, or disproofs. In 1859, Riemann had the idea to define Euler's function ε(x)=∑m^x for all complex numbers s=x+iy by analytic extension. This extension is important in number theory and plays a central role in the distribution of prime numbers. There are a number of ways of extending Euler's zeta functio...

Petition for Certiorari Denied Without Opinion – Patent Case 88-308. Re-examination of Patents in District Courts. 35 USC 302 et. seq.

It is well known that finding large prime numbers is difficult.i We have no algorithm to find primes although we have algorithms to narrow the search. The two main tools we have are theory and empirical data both supported by computers. But, with increased number size of numbers computation becomes prohibitive in time and resources. For small prime numbers, it is easy as we have exhaustively tested all less than 20 digit numbers through some fast probable prime tests and found no false res...

Is there a procedure or algorithm that can decide whether statements, mathematical or non-mathematical, are true or false, win or draw? The broader decision problem can be stated as follows: Even though a mathematical or non-mathematical statement is undecidable in general, it may be possible to find a special algorithm that makes a computer model stop or checkmate. A computer model stops when a true or false decision is made. A computer model game ends when a checkmate win or draw occurs....

Proof that Beal And Fermat Triplets Cannot Exist. This is a single page proof of Fermat's Last Theorem and Beal's conjecture in terms of Euclid's formulas for triplets.