Ziyang Liu

Two problems in comparative prime number theory: the five-way race modulo 11, and the sign of the integrated prime counting error

We resolve two problems of Hamieh, Kadiri, Martin and Ng in comparative prime number theory. Under GRH and the usual linear-independence hypothesis, we compute all 120 logarithmic densities in the five-way prime number race among the quadratic residues modulo 11, prove that they...

An Arithmetic Defect beyond the Symplectic Trace Wall

We study the fixed-distance range beyond the symplectic trace wall for quadratic L-functions over function fields. Using Wang's ratios theorem and a four-swap calculation, we identify an arithmetic Euler factor in the limiting second moment. For distance three, the first correcti...

Two problems in comparative prime number theory: the five-way race modulo 11, and the sign of the integrated prime counting error

We resolve two problems of Hamieh, Kadiri, Martin and Ng in comparative prime number theory. Under GRH and the usual linear-independence hypothesis, we compute all 120 logarithmic densities in the five-way prime number race among the quadratic residues modulo 11, prove that they...