Nardelli, Michele (2008) On the physical interpretation of the Riemann zeta function, the Rigid Surface Operators in Gauge Theory, the adeles and ideles groups applied to various formulae regarding the Riemann zeta function and the Selberg trace formula, padic strings, zeta strings and padic cosmology and mathematical connections with some sectors of String Theory and Number Theory. Dip.Sc.TerraDip.Matem.Unina. (Unpublished)

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Abstract
This paper is a review of some interesting results that has been obtained in the study of the physical interpretation of the Riemann zeta function as a FZZT Brane Partition Function associated with a matrix/gravity correspondence and some aspects of the Rigid Surface Operators in Gauge Theory. Furthermore, we describe the mathematical connections with some sectors of String Theory (padic and adelic strings, padic cosmology) and Number Theory. In the Section 1 we have described various mathematical aspects of the Riemann Hypothesis, matrix/gravity correspondence and master matrix for FZZT brane partition functions. In the Section 2, we have described some mathematical aspects of the rigid surface operators in gauge theory and some mathematical connections with various sectors of Number Theory, principally with the Ramanujan’s modular equations (thence, prime numbers, prime natural numbers, Fibonacci’s numbers, partitions of numbers, Euler’s functions, etc…) and various numbers and equations related to the Lie Groups. In the Section 3, we have described some very recent mathematical results concerning the adeles and ideles groups applied to various formulae regarding the Riemann zeta function and the Selberg trace formula (connected with the Selberg zeta function), hence, we have obtained some new connections applying these results to the adelic strings and zeta strings. In the Section 4 we have described some equations concerning padic strings, padic and adelic zeta functions, zeta strings and padic cosmology (with regard the padic cosmology, some equations concerning a general class of cosmological models driven by a nonlocal scalar field inspired by string field theories). In conclusion, in the Section 5, we have showed various and interesting mathematical connections between some equations concerning the Section 1, 3 and 4.
Item Type:  Article 

Subjects:  500 Scienze naturali e Matematica > 510 Matematica 
Depositing User:  Michele Nardelli 
Date Deposited:  08 Oct 2008 
Last Modified:  20 May 2010 12:01 
URI:  http://eprints.bice.rm.cnr.it/id/eprint/625 
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