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After studying Herstein's books for Algebra (undergraduate and graduate) alongside some books in Analytic Number Theory, I decided to study Algebraic Number Theory as well. I read a recommendation on MSE (I don't remember the link) for Alaca's wonderful book and I just finished it!

My research interest is on Euler's constant and I was wondering do I have study more advanced book(s) on Algebraic Number Theory?

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    $\begingroup$ It is a bit unclear what you are asking. Your interest in the Euler-Mascheroni constant is driven by the fact that you might want to prove its irrationality? In such a case I would rather suggest a crash course in Diophantine Approximation and Beuker integrals. $\endgroup$ – Jack D'Aurizio Aug 23 '18 at 23:08
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    $\begingroup$ But I would also suggest you to stay away from long-standing open problems. They might be rewarding, but they might be extremely disappointing, too. $\endgroup$ – Jack D'Aurizio Aug 23 '18 at 23:10
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    $\begingroup$ @JackD'Aurizio, Thank you for your comment. When I first saw Euler-Mascheroni constant was in Advanced Calculus and my hope that I might be able to prove its irrationality lead me to learn many areas of mathematics and also increased my interest in abstract algebra which I didn't like it beforehand. In short, it has many good 'side-effects'! :) $\endgroup$ – user231343 Aug 24 '18 at 8:27
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    $\begingroup$ @JackD'Aurizio, I have studied the two vols Analytic Number Theory by Apostol, Hardy's number theory, Gamma by Havil, Making Transcendence Transparent by Burger, Algebraic Number Theory by Alaca and introductory texts in continued fractions. I can read some of the papers written on EMC but should I learn more subjects in math to have broader knowledge and better tools? Thanks. $\endgroup$ – user231343 Aug 24 '18 at 8:34
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    $\begingroup$ @D.R., I want to learn advanced Algebraic Number Theory oriented to help with research on Euler's constant, i.e. if undergrad book Algebraic Number Theory is enough so I won't study a more advanced one. PS - I wanted to post a similar question, to avoid duplicate question I set the bounty on this, instead. Note that the OP is "dead" so please add L.G. for I'd be noticed. Thanks! :) $\endgroup$ – L.G. Mar 2 at 21:15

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