0

I have just finished the book "Tom M. Apostol - Introduction to Analytic Number Theory". My aim is to reach to graduate level to do research, especially on Rationality/Irrationality and Algebraic/Transcendentality of Euler-Mascheroni Constant, but articles are not only too advanced to study after Apostol's book, but also I don't think that they are readable by just studying Apostol's book at all for a self-learner like me. Please someone tell me a book for Analytic Number Theory more advanced than Apostol's book but readable esp. for self-learning . Thanks a lot.

PS I am not sure if the books recommended here could be more helpful for research on Euler-Mascheroni Constant. I have also studied the book Havil, J.: Gamma: Exploring Euler's Constant and some elementary materials in continued fractions..

Community
  • 1
  • 1
    you can read the book by Ovidui Furdui on Fractional Parts Integral to improve your real analysis knowledge on integrals since it directly relates to sum and convergence of integral and finding sum and estimating sums. – DeepSea Jun 17 '16 at 14:51
  • 1
    The varying degrees of algebraicness of $\gamma$ is very narrow for a research topic. – anomaly Jun 17 '16 at 14:53
  • @anomaly, sorry I don't understand which one do you mean: algebraicness of γ is less important in research or discussions on books about it are little? –  Jun 17 '16 at 14:56
  • @DeepSea, is this https://www.amazon.com/Limits-Fractional-Part-Integrals-Mathematical/dp/1461467616 you mean? If so, does it have a solution book? thanks. –  Jun 17 '16 at 15:04
  • 1
    I recommend you do Murty's book on analytic number theory, which has exercises & solutions. If you want specifically to make a study of transcendental number theory, there is an introductory book by Burger and Tubbs. There is a readable book by Murty & Rath with a lot of exercises, and a more advanced one by Baker. There is another one by Gelfond (which is an inexpensive Dover edition) but I am not familiar with it. – John M Jun 17 '16 at 19:16

0 Answers0