Euler-Kronecker constants for cyclotomic fields

2022/03/07 by Hong, Letong, Ono, Ken, Zhang, Shengtong
#11M06 #11N37 #11R18 #11R42 #11Y60 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.03589

Abstract

The Euler-Mascheroni constant γ=0.5772… is the K=ℚ example of an Euler-Kronecker constant γ_K of a number field K. In this note we consider the size of the γ_q=γ_Kq for cyclotomic fields K_q:=ℚ(ζ_q). Assuming the Elliott-Halberstam Conjecture (EH), we prove uniformly in Q that (1)/(Q)∑_Q

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