Need to complete the the dissertation on Non-Archimedean Analysis(P-adic analysis). The description of the topic is following:
"Let $p$ be a prime number. p-adic numbers appear in a very similar way to real numbers as the completion of the field of rational numbers. In the case of real numbers we use the usual metric given by the modulus of distance between two given rational numbers. In the case of p-adic numbers we must use another, so-called non-archimedean, metric given by the p-adic distance: two integral rational numbers are p-adically close if their difference is divisible by a large power of prime number p. The theory of p-adic numbers is based on elementary number theory and at the same time contains many results which are similar to the corresponding properties of usual real numbers.
In particular, the p-adic numbers can be used for developing all basic concepts of the traditional calculus: functions, limits, derivatives, integrals, infinite series and so on. For example, in the field of 3-adic numbers the series 1+3+9+27+81+... converges and its sum equals(!) minus 1/2. One can introduce an analogue of the usual exponential function exp(x), which satisfies many usual properties, but the corresponding infinite Taylor series does not converge for all x. There is very interesting theory of p-adic integration. The project will be concerned with the study of basic properties of p-adic numbers and functions, p-adic differential equations, the construction of p-adic integration and so on."
In other words, I need to analyse different functions(exponential, binomial, log) and compare these functions to the same functions on the field of real numbers. Please see attached the poster I've done. It is basically a short explanation of my dissertation. But some chapter on p-adic integration might be needed as well. It is 3rd year dissertation and has to be written at that level.
Also, the dissertation has to be written in Latex.
p-adic analysis compared with real, by S. Kapok
p-adic numbers, p-adic analysis, and zeta-functions, by N. Koblitz
p-adic analysis and mathematical physics, by V. S. Vladimirov, I. [url removed, login to view], and E. [url removed, login to view]