The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann's zeta-function which are sufficiently strong to break the density hypothesis for Re s>7/8.Apart from...The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann's zeta-function which are sufficiently strong to break the density hypothesis for Re s>7/8.Apart from a simple but ingenious idea of Halász the proof uses only classical knowledge about the zeta-function,results known for at least hundred years.展开更多
Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a ration...Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a rational function on the Riemann sphere with branch data ■ if and only if max(m1,...,ml)<d/GCD(a1,...,ap,b1,...bq),As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.展开更多
基金supported by the National Research Development and Innovation Office of Hungary,NKFIH,KKP 133819。
文摘The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann's zeta-function which are sufficiently strong to break the density hypothesis for Re s>7/8.Apart from a simple but ingenious idea of Halász the proof uses only classical knowledge about the zeta-function,results known for at least hundred years.
基金supported in part by the National Natural Science Foundation of China(grant no.11426236)The second author was supported in part by the National Natural Science Foundation of China(grant nos.11571330 and 11971450)the Fundamental Research Funds for the Central Universities.
文摘Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a rational function on the Riemann sphere with branch data ■ if and only if max(m1,...,ml)<d/GCD(a1,...,ap,b1,...bq),As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.
