If you please share the link of described preprint.

@Muhammad Shahnewaz Bhuyan, yes with pleasure:

https://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/Marcolli-NTphysics.pdf

The journal "Communications in Number Theory and Physics" (https://www.intlpress.com/site/pub/pages/journals/items/cntp/_home/_main/index.php) publishes articles regarding the relationship and dynamics between the two fields.

Algebra & number theory is a concept in Mathematics that deal with the study of the types and properties of numbers. Physical science involves mathematics in all circumstances and is dependent on theory of numbers for reading and study. Physical science relies on tests, hypotheses, and numbers. Physics and mathematics are two subjects that are intertwined. Mathematics is a tool that physicists use to solve physical problems involving standard units of measurement, quantities (scalar and vector), forces, work done and energy among others.

I think a connection can be found in the Langlands Program.

also, free compact bosons are related to quadratic forms and hence lattices.

check this link: Number theory and physics - MathOverflow

https://mathoverflow.net/questions/224263/number-theory-and-physics

See in the paper below how the oscillations of the metaphysical pendulum are connected with the Riemann Zeta function and with the Schrodinger equation. There must be a connection with number theory somewhere nearby.

Preprint Chaotic dynamics of an electron

I think the residual fields $p^{n}$ can be drawn from the fact that the non-trivial zeros of the Riemann zeta function deliver a uniform distribution of fractional fractions of ZetaZero*log(n), where ZetaZero is an arbitrary root of the Riemann zeta function.

Dear Igor,

with respect to approach the primary issue(s) resulting from your question from the mathematical side (based on algebraically first order multiplicative equations describing a simple integer geometric exact model of spacetime) iSpace theory is to derive constants of nature from such first principles, most important the rarely used and often overlooked so called "changed distance definition" as the main basis for creating geometric, algebraic and hence with this strict numeric constraints.

Using this model iSpace theory showed (please see my RG project home via the link given below) 50+ constants of nature can be computed in exact algebraic form, resulting in model intrinsic zero error bar value predictions fully complient to past and current CODATA measurement results.

Attacking this important problem from this side - not searching for some abstract geometric basis for theirs models (like maybe String theory or virtual particles of QED/QCD) having to input such constants of nature to have their model make sense, iSpace theory choose the reverse approach to calculate these from strict integer geometric first principles deducing the possible geometry of spacetime from the derived result equations of the individual constants (like e, h, alpha, R, a0, re, G, ...) in two fully different unit systems - iSpace-SI (fully MKS/A-SI value compatible) and iSpace-IQ, the first of its kind to get away without any human artifacts whatsever (yet still staying fully lab compatible).

While its hard to believe things "down there" in the quantum arena could be that simple when analyzed this way, they fortunately are - verify it yourself! So for more information please take the little additional time to have a look in my project summary (first) and maybe if interested into the links below (in order of raising complexity = time to read):

Project:

https://www.researchgate.net/project/iSpace-Exact-quantum-geometric-value-of-primary-constants-of-nature

Papers:

https://www.researchgate.net/publication/271854188_iSpace_-_NKS_in_a_Spiral_Honeycomb_Mosaic https://www.researchgate.net/publication/271854024_iSpace_-_Deriving_G_from_a_e_R_m0_and_Quantum_of_Gravitational_Force_Fg https://www.researchgate.net/publication/271854031_iSpace_-_Exact_Symbolic_Equations_for_Important_Physical_Constants_-_SI_Table https://www.researchgate.net/project/iSpace-Exact-quantum-geometric-value-of-primary-constants-of-nature https://www.researchgate.net/publication/361800687_iSpace_-_Quantization_of_Time_in_iSpace-IQ_Unit-System_by_16961_iSpace-Second

I am sure one - after truly reading into this - cannot avoid to agree to see the some deep connection between algebra, number theory and physics!

Thanks for your very interesting and imho important question,

Christian

Dear Mohamed Mahmoud Chems-Eddin, very sorry to mismatch you as the originator of this RG question with the reply of Igor Bayak due to unlucky HTML formatting as visible when typing my reply above. Sorry for any possibly confusion my mistake might have caused. Christian

Hi, very Good Question!

Here is my "two cents":

1. my paper "Hydrogen Atom and Elliptic Curve" (aka HEC), delivered on Quantum Mechanics Conference in Paris September 2019, established the correspondence between Rational Points on Special Elliptic Curve (God's Curve as I called it) and Energy levels (aka bound states) of ALL Hydrogenic Atoms in the Universe!

The New Equation of Quantum Elliptic Curve (Two Linked Elliptic Curves actually) I managed to derive in October 2020, turned out to contain the Quantum Entanglement Mechanism!

See version 3.0 of my paper QEC attached, with two methods that can be used to change state of either One or Both particles making up EPR-pair (aka Bell state).

2. Conjecture formulated in my new paper "Motley String Theory Overview" (see MST project on my profile) goes like this: Virasoro Algebra of String oscillators can be transformed to a certain Elliptic Curve (or two linked Elliptic Curves, like in HEC paper above), which may contain Energy levels (aka mass spectra) of Fermionic and Bosonic Strings respectively!

If proved correct, this may turn Motley String Theory into our Theory of Everything!

"Elliptic Curve Dynamics" Program - paper is Invitation to this line of my research.

ALL four Papers are available on my RG profile and they are also attached to this reply for your convenience.

Everyone working with Virasoro algebra, KdV Solitons, String Theory is welcome to join in and contribute their own results!

This Subject is HUGE and Requires OUR Cooperation to be Understood!

Best regards,

George Yury Matveev

www.matveev.se

Hi Mohamed,

I have a long lasting interest on this subject. Good luck.

https://www.researchgate.net/profile/Michel-Planat

Dear mohammed. We can build a modle by using the numbers theory rules. This model can be explained the cosmic phenomena like the motion and distribution of objects , specify the Location and amount of the dark energy and dark matter....... .

One more thing,

the most recent update (today 22 March 2023) on Motley String Theory

https://www.researchgate.net/project/Motley-String-Theory may give you an Idea where Prime Numbers are coming from

and How they are Generated! Sounds Exciting? Have a look and become one of the first illuminated

with the “know how” ;-) Best regards, George Matveev www.matveev.se

New web page MSTPrimeNumberGenerator has just been added to my personal web site:

http://matveev.se/math/MSTPrimeNumberGenerator.htm

The page contains some details and the link to MST project update on RG where the new paper Prime Number Generator has just been posted.

Welcome!

Best regards,

George Yury Matveev

www.matveev.se

Hi Michel,

Good question!!! What about this?

Article Ramanujan's influence on string theory, black holes and moonshine

My best wishes....

Thank you. It is a good reference. Michel.

One more thing:

my most recent paper Prime Number Generator (aka PNG)

demonstrated how one can Generate All Primes up to arbitrarily Big N,

using Motley String Theory (aka MST) physical principles!

Paper also provides basic details of possible Software Implementation of the PNG in Java programming language.

This serves as one more confirmation that Motley String Theory is our Best Candidate for the Theory of Everything!

Your comments and feedback are Very Welcome!

Best regards,

George Yury Matveev

www.matveev.se

Partition functions have applications in quantum physics counting states and Ramanujan's mock-theta functions are connected to the mathematics of black holes.