Abstract
Let P be a finite set of finite rational primes. In this article, we prove the existence of infinitely many positive integers \(n_i\) such that corresponding to each such integer \(n_i\), there are infinitely many number fields L (both totally real and totally imaginary) of degree \(n_i\) which ramify exactly at \(|P|+1\) finite rational primes and admitting an infinite p-class field tower, for all \(p \in P\), simultaneously.
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Acknowledgements
I would like to thank Prof. V. Kumar Murty for intoducing this research area during his visit to HRI in October 2019. I am also very grateful to Prof. R. Schoof for his comments, suggestions and inspiring conversation on a preliminary version of this article and for a proof of Theorem 3.1. I am also indebted to Prof. R. Thangadurai for his fruitful suggestions and for carefully going through the paper. I am also very thankful to my Ph.D. supervisor Prof. K. Chakraborty for his constant support while doing this project. The author is grateful to the anonymous referee for carefully reading this manuscript and giving valuable comments and suggestions which has helped improving the presentation immensely. I gratefully acknowledges the National Board of Higher Mathematics for providing financial support (Order No. 0203/21(4)/2022-R &D-II/10341).
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Mishra, M. Infinite Hilbert class field tower. Res. number theory 9, 49 (2023). https://doi.org/10.1007/s40993-023-00453-x
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DOI: https://doi.org/10.1007/s40993-023-00453-x