Simultaneous large values and dependence of Dirichlet L-functions in the critical strip

2022/11/28 by Inoue, Shōta, Li, Junxian
#11M06 #60B12 #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.15165

Abstract

We consider the joint value distribution of Dirichlet L-functions in the critical strip (1)/(2) < σ< 1. We show that the values of distinct Dirichlet L-functions are dependent in the sense that they do not behave like independently distributed random variables and they prevent each other from obtaining large values. Nevertheless, we show that distinct Dirichlet L-functions can achieve large values simultaneously infinitely often.

Related

• Large values of Dirichlet L- functions inside the critical strip
• Joint value distribution of L-functions on the critical line
• On the Value Distribution of Two Dirichlet L-functions
• Upper bounds on L-functions at the edge of the critical strip
• A note on entire L-functions