A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for...A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for each local Hankel transformation of order 1/2.An S-local Connes type trace formula is derived for the S-local Hankel transformation of order 1/2.These formulas are generalizations of Connes' corresponding trace formulas in 1999.展开更多
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system...In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.展开更多
Let K be a p-adic local field.We study a special kind of p-adic Galois representations of it.These representations are similar to the Galois representations occurred in the exceptional zero conjecture for modular form...Let K be a p-adic local field.We study a special kind of p-adic Galois representations of it.These representations are similar to the Galois representations occurred in the exceptional zero conjecture for modular forms.In particular,we verify that a formula of Colmez can be generalized to our case.We also include a degenerated version of Colmez’s formula.展开更多
文摘A local Hankel transformation of order 1/2 is defined for every finite place of the field of rational numbers.Its inversion formula and the Plancherel type theorem are obtained.A Connes type trace formula is given for each local Hankel transformation of order 1/2.An S-local Connes type trace formula is derived for the S-local Hankel transformation of order 1/2.These formulas are generalizations of Connes' corresponding trace formulas in 1999.
基金Supported by Shandong Provincial Natural Science Foundation under Grant Nos. ZR2011AQ017 and ZR2010AM028
文摘In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.
基金supported by National Natural Science Foundation of China(Grant No.11271021)
文摘Let K be a p-adic local field.We study a special kind of p-adic Galois representations of it.These representations are similar to the Galois representations occurred in the exceptional zero conjecture for modular forms.In particular,we verify that a formula of Colmez can be generalized to our case.We also include a degenerated version of Colmez’s formula.
