In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω=Ω\∪_(j=1^(m))Ω_(j),where Ω and {Ω_(j)}_(j=1^(m)■Ω are bounded ...In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω=Ω\∪_(j=1^(m))Ω_(j),where Ω and {Ω_(j)}_(j=1^(m)■Ω are bounded pseudoconvex domains in ℂ^(n) with smooth boundaries,and Ω_(1),…,Ω_(m) are mutually disjoint.The main results can also be quickly obtained by virtue of[5].展开更多
The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R<sup>2&l...The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R<sup>2</sup> will be studied, helping therefore to solve a usual boundary value problem for the Cauchy-Riemann operator.展开更多
In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the cr...In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.展开更多
文摘In this note,we mainly make use of a method devised by Shaw[15]for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω=Ω\∪_(j=1^(m))Ω_(j),where Ω and {Ω_(j)}_(j=1^(m)■Ω are bounded pseudoconvex domains in ℂ^(n) with smooth boundaries,and Ω_(1),…,Ω_(m) are mutually disjoint.The main results can also be quickly obtained by virtue of[5].
文摘The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R<sup>2</sup> will be studied, helping therefore to solve a usual boundary value problem for the Cauchy-Riemann operator.
文摘In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) for all z∈C, and we prove: 1) that G and the Riemann zeta function ζ have exactly the same zeros in the critical region D:= {z∈C:ℜz∈(0,1)};2) the Riemann hypothesis, i.e., that all of the zeros of G in D are located on the critical line := {z∈D:ℜz =1/2};and that 3) all the zeros of the Riemann zeta function located on the critical line are simple.
