 

Lior BarySoroker
and Françcois Legrand
On the number of ramified primes in specializations of function fields over Q
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Published: 
October 23, 2018. 
Keywords: 
Ramification, function field extension, specialization, central limit theorem. 
Subject: 
11K65, 11N37, 11N56, 11R44, 11R58, 12E05, 12E25. 


Abstract
We study the number of ramified prime numbers in finite Galois extensions of Q obtained by specializing a finite Galois extension of Q(T). Our main result is a central limit theorem for this number. We also give some Galois theoretical applications. 

Acknowledgements
The first author is partially supported by the Israel Science Foundation (grant No. 40/14). The second author is partially supported by the Israel Science Foundation (grants No. 40/14 and No. 696/13).


Author information
Lior BarySoroker:
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv, Tel Aviv 6997801, Israel.
barylior@post.tau.ac.il
Françcois Legrand:
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv, Tel Aviv 6997801, Israel, and
Department of Mathematics and Computer Science
The Open University of Israel
Ra'anana 4353701, Israel.
flegrand@post.tau.ac.il

