Background of question ( Background is somewhat related to this question Asking about how to minimize the effect of a not so good thesis due to abandoning by supervisor without even telling in Phd Application Form but question is entirely different)

I am a masters 2nd year student( 4 th semester)in mathematics .During my masters degree I self studied 3 books of number theory ( 1 elementary,2 analytic)because I was really interested in learning it and no faculty in my Institute is specialized in it( most people in my Institute are specialized in Applied Mathematics) . I am in an 3rd world country.

I want to do phd in number theory in Europe. So, for my Masters thesis I wrote to one of professors in a top Institute in my country and she said yes.I visited her Institute in January,2020 for 8 days but she abandoned me and didn't even bothered to tell as she didn't replied my e - mails and despite the fact that she gave me a research paper in January to study and after completing it I e-mail her on 20 Feb asking her to tell me which paper to study now/ problem to work and when should I visit her Institute again . I e mailed her on 29 Feb, 7 March, 25 March, 4April.( in between I read 2 papers to know a bit more about the work in the area).

Also I am 100% sure that she is not suffering from covid. So, I talked to a professor in my institute and he took absolutely no interest in helping me and send prepare a report from the paper what you have studied and hung up.

I have read 4 papers in analytic number theory till now( all are related to 1st paper given by professor) . And i am thinking of reading another research paper in analytic number theory but it's related to a different problem if time permits. But i have not done any original work like writing a research paper or proving a theorem.

My questions are 1.what kind of work is expected in a Masters thesis by the Admission committees of European Institutes ?

2.Is is necessary to have a publication or original work like proving some results for applying to Europe?

3.Is is a good idea to have 5 th paper not related to first 4 papers despite the fact that both are parts of analytic number theory?

Please guide. I have no other sources of help. I wanted to work really nicely for the thesis but things changed completely due to negligence of that professor. Even the professor of my Institute didn't bothered.

I am in desperate need of guidence.

Background of question ( Background is somewhat related to this question Asking about how to minimize the effect of a not so good thesis due to abandoning by supervisor without even telling in Phd Application Form but question is entirely different)

I am a masters 2nd year student( 4 th semester)in mathematics .During my masters degree I self studied 3 books of number theory ( 1 elementary,2 analytic)because I was really interested in learning it and no faculty in my Institute is specialized in it( most people in my Institute are specialized in Applied Mathematics) . I am in an 3rd world country.

I want to do phd in number theory in Europe. So, for my Masters thesis I wrote to one of professors in a top Institute in my country and she said yes.I visited her Institute in January,2020 for 8 days but she abandoned me and didn't even bothered to tell as she didn't replied my e - mails and despite the fact that she gave me a research paper in January to study and after completing it I e-mail her on 20 Feb asking her to tell me which paper to study now/ problem to work and when should I visit her Institute again . I e mailed her on 29 Feb, 7 March, 25 March, 4April.( in between I read 2 papers to know a bit more about the work in the area).

Also I am 100% sure that she is not suffering from covid. So, I talked to a professor in my institute and he took absolutely no interest in helping me and send prepare a report from the paper what you have studied and hung up.

I have read 4 papers in analytic number theory till now( all are related to 1st paper given by professor) . And i am thinking of reading another research paper in analytic number theory but it's related to a different problem if time permits. But i have not done any original work like writing a research paper or proving a theorem.

My questions are 1.what kind of work is expected in a Masters thesis by the Admission committees of European Institutes ?

2.Is is necessary to have a publication or original work like proving some results for applying to European Institutes .

Please guide. I have no other sources of help. I wanted to work really nicely for the thesis but things changed completely due to negligence of that professor. Even the professor of my Institute didn't bothered.

I am in desperate need of guidence.