In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus ...In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.展开更多
In this paper,new proofs of two functional relations for the alternating analogues of Tornheim's double zeta function are given.Using the functional relations,the author gives new proofs of some evaluation formula...In this paper,new proofs of two functional relations for the alternating analogues of Tornheim's double zeta function are given.Using the functional relations,the author gives new proofs of some evaluation formulas found by Tsumura for these alternating series.展开更多
文摘In this paper, the author applies adjacent lattice method and Siegel mass formula to determine the classes of positive definite unimodular lattices of rank 4 over Z , and obtains that the class number of unit genus gen( I 4 ) is nine and the class number of even unimodular lattices is three, and also gives the representative lattices of each class.
基金supported by the National Natural Science Foundation of China(No.11471245)the Shanghai Natural Science Foundation(No.14ZR1443500)
文摘In this paper,new proofs of two functional relations for the alternating analogues of Tornheim's double zeta function are given.Using the functional relations,the author gives new proofs of some evaluation formulas found by Tsumura for these alternating series.
