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

A discussion of a rationality and continuity related to Theta Functions by using the summation of Poisson | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A discussion of a rationality and continuity related to Theta Functions by using the summation of Poisson Akram Louiz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2378274/v4 This work is licensed under a CC BY 4.0 License Status: Posted Version 4 posted You are reading this latest preprint version Show more versions Abstract Mathematical philosophy is built by defining logical concepts such as the concept of infinity and the concept of continuity. Hence, mathematicians are not those who can calculate, but those who can understand the mathematical concepts and can develop them in order to make new mathematical findings or to transform an hypothesis into a philosophical truth. However, mathematicians are also alarmed scientists who can verify doubted formulas by disproving a mathematical proof or finding a counterexample. It is therefore false to think that mathematicians can’t surprise nowadays 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 Series summation Poisson Theta function rational irrational limit logic approximation calculus analysis Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 4 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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