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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 previous knowledge of Sieve Theory. Although I know about some books in sieve theory like Montgomery ( Topics in multiplicative number theory) , Friedlander and Iwaniac ( Sieve theory: A musical) but my Institute only accepts research papers in masters thesis.

So, can any researcher here suggest 2 research papers which led to the beginning of the subject of sieve theory. I will study them and present them along with the papers I have already studied.

I have searched in past 4-5 days for some papers in different domains of ANT over web pages of different professors and some other websites but it doesn't lead me much as I am just a beginner in this field.

Thanks!

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    $\begingroup$ I downvoted because your lifestory has no relevance and is not suitable on MO. $\endgroup$
    – user6976
    Apr 18, 2020 at 16:37
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    $\begingroup$ You also mentioned other things like "being abandoned by a professor" and that you did not manage to read a paper and that you want to talk about something but do not know what it is. $\endgroup$
    – user6976
    Apr 18, 2020 at 16:48
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    $\begingroup$ "I started working on masters thesis as per guidance of a professor not of my Institute who abandoned me and didn't even bothered to tell." Yes, you've told us this several times now. May I suggest that you find another professor, at your institute, who will give you an idea for a master's thesis & help you with it? Trying to write a thesis without supervision is asking for trouble, and MathOverflow is not a substitute for a supervisor. $\endgroup$ Apr 19, 2020 at 0:02
  • $\begingroup$ I have nothing to contribute, concerning sieve theory. Have you considered working in something other than Number Theory? Have you considered transferring to another institute? These may not seem like attractive options to you, but they may be better than what you are trying to do. $\endgroup$ Apr 20, 2020 at 5:52
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    $\begingroup$ Flooding MO with edits of your old questions that already have accepted answers seems to me to be an abuse of this website. $\endgroup$ Sep 9, 2020 at 5:11

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Sieve theory as such is generally considered to have started with Brun's 1915 and 1919 papers. The titles are "Über das Goldbachsche Gesetz und die Anzahl der Primzahlpaare" and ""La série $1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+\cdots$, où les dénominateurs sont nombres premiers jumeaux est convergente ou finie".

Legendre's sieve predates Brun's sieve, but it seems to be thought of more of a precursor to sieve theory than anything else.

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    $\begingroup$ can you please tell where I can find original paper these? $\endgroup$
    – Arnold
    Apr 19, 2020 at 13:40
  • $\begingroup$ Or English translations but of both of these papers!! I searched the internet. I can find A book "Goldbach conjecture " But it will not have papers (original ) Although 1st paper is given in its references. But i have no clue about 2 nd? Can you please tell where they are available!! $\endgroup$
    – Arnold
    Apr 19, 2020 at 13:53
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    $\begingroup$ The 2nd paper is at gallica.bnf.fr/ark:/12148/bpt6k486270d/f138.item.r=brun $\endgroup$ Apr 20, 2020 at 7:09
  • $\begingroup$ @Gerry Myerson thanks for the help. $\endgroup$
    – Arnold
    Apr 20, 2020 at 10:11

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