I recently started writing a research paper and I have the following questions:
1.) What level of mathematical knowledge is the exclusion of a lemma to explain a particular outcome. For example, if a trig is involved, a lemma is needed to show where the roots of a given trigger function are. It seems pretty elementary, but on the other hand, the reader may be confused by lack of explanations and not focus on what you are trying to deliver.
2.) When is a proof of a theorem required? For example, if the proof of a particular sentence is straightforward and uses only elementary operations (ie, +, -, x, /), the proof is really necessary. If not, you can call that sentence a lemma.
3.) Should you tell the reader when an equation or formula was last used? Alternatively, you should indicate that a particular formula is used continuously and frequently throughout the work and, if so, how.
4.) If you refer to a numbered equation, it is best to write "See Equation 1. We see that …", "In Equation (1) we can see that …", "In (1), We can see that … "or" See (1). We can see that … ". In addition, should equations that are used only in proof for a sentence be numbered?
5.) How many people should check your work before deciding to submit it to a journal?
6.) Which publication method is better for an author writing his first paper: ArXiv or a recent journal? If magazine, what are some good ones for number theory, which are less strict in the selection of the works to be published?
I realize that there are many questions that may require lengthy explanations. So you can only answer 1 to 3. If this is more appropriate for another stack site, please forward me in the comments rather than down. I would be fine with deleting and posting elsewhere. Many thanks for the help!