Dmitri Martila

Proof of the Riemann Hypothesis.

There are many unproven hypotheses in science, e.g., abc conjecture. Who will prove them all? Some will be done in conventional Research because we still have time left. But a large part will be solved or answered by God. But who will answer the question of God's existence? Let me try.

The tremendously complicated, 1000 pages long proof of the abc conjecture seems to be peer-reviewed, but not accepted by the mainstream community. Therefore, a one-page proof of the conjecture, even if mistrusted for being short, has to be considered as a serious attempt to prove the conjecture.

A new derivation of Navier-Stokes equations is suggested. A flaw in the old derivation is found. The turbulence is explained.

A criterion given by Jean-Louis Nicolas is used to offer a proof for the Riemann Hypothesis in a straightforward way.

Proof of Riemann Hypothesis via Nicolas criterion.

Suppose the Riemann Zeta function is multiplied by two arbitrary functions, and the resulting functions' values are equated at symmetrical points concerning the critical line ℜ s = 1/2. In that case, the resulting system of four equations has to give the positions of the Zeta function's zeros. However, since the functions are arbitrary, the positio...

The Riemann Hypothesis is of great interest in number theory because it implies results about the distribution of prime numbers. Explanations why the real part of Zeta function zeroes is always being seen on the 1/2 line. First explanation is the reference to my preprint at arXiv.org. MSC Class: 11M26, 11M06.

It is not known if this constant is irrational, let alone transcendental. The famous English mathematician G. H. Hardy is alleged to have offered to give up his Savilian Chair at Oxford to anyone who proved gamma to be irrational, although no written reference for this quote seems to be known. Hilbert mentioned the irrationality of gamma as an unso...

All classical systems must be Galilean invariant, but Navier-Stokes equations are not. The solution is the correct derivation of Navier-Stokes equations. MSC Class: 35Q30, 00A27, 00A05, 00A30, 03F40, 03F99, 00A35.

I have written a solution.

I have written a solution.

I have written a new proof of Riemann Hypothesis.

A simple argument proves the conjecture.

A simple argument proves the Beal Conjecture. There is a million-dollar prize for solving the Beal Conjecture.

A simple proof confirms Riemann, Generalized Riemann, Collatz, Swinnerton-Dyer conjectures, and Fermat's Last Theorem.

I have written a solution to Navier—Stokes Millennium Prize problem.

Several crucial properties of abc conjecture are presented and proven. One of the resultsis that the ternary Goldbach Conjecture implies the existence of three numbers \((a, b, c)\) that satisfy the abc conjecture for an arbitrary value of the sum \(c=a+b\).

Several short proofs of the Riemann Hypothesis.

Using geometric considerations, we provided a clear derivation of the integral representation for the error function, known as the Craig formula. We calculated the corresponding power series expansion and proved the convergence. The same geometric means finally assisted in systematically deriving useful formulas that approximated the inverse error...

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. O...

The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function or the cumulative distribution of the normal distribution, cannot be expressed by analytic functions. This is...

About set theory.

Flat earthers and Globe earthers are not stupid. But both kind of people do not see the whole situation.

In this note, I am proving the Riemann hypothesis.

It is well known that the Gauss (or Poisson or Euler) integral cannot be analytically calculated if the area of integration has a finite boundary. In this publication, you will take part in the real miracle of actually calculating this "impossible" integral. As for 2021 AD, only a diverging sum for this integral is known, but I proudly present the...

You are free not to get enlightened about the fact in the title. But please pay respect to new dispositions of the Navier-Stokes equations and research methods in this note.

Using the brand new and powerful Martila method, I am able to: give a proof of the Riemann hypothesis; and to discuss the conjecture given by Birch and Swinnerton-Dyer; and to extract information about Yang-Mills Theory. As a bonus, there is a demonstration of the abc conjecture. You are free not to get enlightened about these facts. But please pay...

In this short note, I provide a proof for the Riemann Hypothesis. You are free not to get enlightened about that fact. But please pay respect to new dispositions of the Riemann Hypothesis and research methods in this note. I start with Dr. Zhu who was the first to show me that instead of the known 40 %, the maximum percentage of the zeroes of the R...

The efficiency of energy transformation of overdamped Brownian particles in a tilted periodic sawtooth potential driven by a nonequilibrium three-level noise and an additive thermal noise is considered analytically. All the physical results are computed by means of exact formulas. It is established that in certain parameter region the dependence of...

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and som...

The noise-flatness-induced hypersensitive transport of overdamped Brownian particles in a tilted ratchet system driven by multiplicative nonequilibrium three-level Markovian noise and additive white noise is considered. At low temperatures, the enhancement of current is very sensitive to the applied small static tilting force. It is established tha...

Transport of Brownian particles in a simple sawtooth potential subjected to both unbiased thermal and nonequilibrium symmetric three-level Markovian noise is considered. The effects of three and four current reversals as a function of temperature are established in such correlation ratchets. The parameter space coordinates of the fixed points assoc...

Multinoise correlation ratchets with a simple sawtooth potential are considered. It is proved that in the case of symmetric nonequilibrium three-level Markovian noise the direction and value of the induced current can be controlled by thermal noise. Moreover, it is established that four current reversals (CRs) occur and that for the CRs there exist...