Article Dans Une Revue Asia Mathematika Année : 2024

A discussion of rationality and continuity related to Theta Functions by using the summation of Poisson

Akram Louiz

Résumé

Mathematical philosophy is built by defining logical concepts such as the concept of infinity and the concept ofcontinuity. Hence, mathematicians are not those who can calculate, but those who can understand the mathematicalconcepts and can develop them in order to make new mathematical findings or to transform an hypothesis into aphilosophical truth. However, mathematicians are also alarmed scientists who can verify doubted formulas by disprovinga mathematical proof or finding a counterexample. It is therefore false to think that mathematicians can't surprisenowadays with new findings. This is a mathematical demonstration and discussion concerning a special case of functions related to Theta Functions and it is a logical opportunity for those who study the summation of Poisson. This work starts by using a formula of Poisson in order to make a mathematical representation for the studied function then a new approximation of this case of functions is demonstrated. Furthermore, we discuss the consequences if this studied function gives only irrationals as outputs then we use the definition of the continuity of real functions in order to make a demonstration for the continuity of the same Function. Finally, the lovers of mathematics are invited to understand the demonstrations of this article and the discussions of the continuity contradictions in order to develop new findings related to Theta Functions and the summation of Poisson.

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Dates et versions

hal-04442443 , version 2 (30-07-2024)

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Citer

Akram Louiz. A discussion of rationality and continuity related to Theta Functions by using the summation of Poisson. Asia Mathematika, In press, ⟨10.5281/zenodo.10609879⟩. ⟨hal-04442443⟩
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