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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

1 vote
0 answers
352 views

What are the current directions/topics of research taking place in Analytic Number Theory

I have studied analytic number theory from 2 volumes of Apostol , Lectures in Sieve Theory online and I am thinking of reading some research papers in Number Theory and then try to work on some proble …
Arnold's user avatar
  • 793
2 votes
1 answer
444 views

A deduction in paper of Tanguy Rivoal and Wadim Zudilin which I am unable to think about

This question is related to Paper of Wadim Zudilin and Tanguy Rivoal "A note on odd zeta values". Some users are saying that I should not post question related to papers in MO but site mentions quest …
Arnold's user avatar
  • 793
9 votes
1 answer
779 views

Status of current research in Sieve Theory

I have done a course in Sieve Theory from the notes of Prof. Rudnick. Before this, I did 2 courses in Number Theory from the 2 volumes of Apostol. I don't have any guidance by professor as I am living …
Arnold's user avatar
  • 793
8 votes
1 answer
1k views

Advice: What topics to study now in analytic number Theory( And if there are video lectures(...

I am a person living in a 3rd world country and completed my masters in mathematics in July 2020. Then I began to study some additional topics in Pure Mathematics as I was applying for Ph.D. abroad( I …
Arnold's user avatar
  • 793
1 vote
1 answer
705 views

How to prove a result related to prime number theorem in research paper of Rivoal and Zudilin

Question is ->I am studying research paper: A note on odd zeta values and I am unable to think how to deduce a result which the authors don't prove. This result has to be proved assuming the prime num …
Arnold's user avatar
  • 793
-1 votes
1 answer
370 views

An argument involving integratibility of a research paper of Rivoal

I am self studying a research paper in analytic number theory (Ball and Rivoal - Irrationalité d’une infinité de valeurs de la fonction zêta aux entiers impairs) and I am unable to think about an argu …
Arnold's user avatar
  • 793
3 votes
1 answer
343 views

Unable to deduce an inequality in paper on odd zeta values of Fischler, Sprang and Zudilin

I am a masters student and I am interested in number theory. Due to lockdown I have a lot of time and I thought of reading a research paper in Number theory which is " Many Odd zeta values are irratio …
Arnold's user avatar
  • 793
1 vote
1 answer
222 views

Understanding a deduction in research paper of Sprang, Fischler and Zudilin ("Many Odd zeta ...

I am a master's student interested in number theory. I am reading a research paper in Analytic Number theory which is "Many Odd zeta values are irrational" by Stephane Fischler, Johannes Sprang and W …
Arnold's user avatar
  • 793
-8 votes
1 answer
556 views

A question in paper " A note on Odd zeta values " by Tanguy Rivoal and Wadim Zudilin on page 6

I am studying research paper " A note on odd zeta values " by Tanguy Rivoal and Wadim Zudilin . Note-> This question has been closed 2 times on math.stackexchange . Earlier it was posted on MathOverf …
Arnold's user avatar
  • 793
-3 votes
1 answer
379 views

References of research papers which lead to starting of Sieve Theory

Question - I am thinking to present one or two papers on Sieve Theory in my masters thesis. I will also present 3 other papers on Riemann Zeta Function which I have studied earlier . But I have no p …
Arnold's user avatar
  • 793
2 votes
0 answers
290 views

Resources where one can find open problems in Analytic Number Theory

Edit: I have asked this question separately because I am in need of some resources which focus on analytic number theory only.So, this question is not a duplicate of:Resources where I can find open p …
Arnold's user avatar
  • 793
0 votes
2 answers
525 views

Need help in understanding meaning of a notation and theorem used in research paper due to a...

I thought of utilizing this lockdown period to study research papers in number theory by myself. I began reading the research paper By T Estermann ->" On Goldbach Problem : Proof that Almost all Ev …
Arnold's user avatar
  • 793
16 votes
5 answers
4k views

Resources where I can find open problems in number theory along with their level of difficulty

NOTE: I will not accept an answer because a lot of answers are really good and if anyone want to post under this question later then they are most welcome to post as comment or answer because it will …