5 papers · 1 filter
On -adic Minkowski's Theorems
Yingpu Deng
Dual lattice is an important concept of Euclidean lattices. In this paper, we first give the right definition of the concept of the dual lattice of a -adic lattice from the dual…
On -adic Gram-Schmidt Orthogonalization Process
Yingpu Deng
In his famous book ``Basic Number Theory", Weil proved several theorems about the existence of norm-orthogonal bases in finite-dimensional vector spaces and lattices over local fie…
On Periodicity of Continued fractions with Partial Quotients in Quadratic Number Fields
Zhaonan Wang, Yingpu Deng
The properties of continued fractions whose partial quotients belong to a quadratic number field K are distinct from those of classical continued fractions. Unlike classical contin…
Combinatorial Sums $\sum_{k\equiv r(\mbox{mod} m)}{n\choose k}a^k$ and Lucas Quotients (II)
Jiangshuai Yang, Yingpu Deng
In [16], we obtained some congruences for Lucas quotients of two infinite families of Lucas sequences by studying the combinatorial sum $$\sum_{k\equiv r(\mbox{mod}m)}{n\choose k}a…
Representing Primes as the Form in Some Imaginary Quadratic Fields
Chang Lv, Yingpu Deng
We give criteria of the solvability of the diophantine equation over some imaginary quadratic fields where is a prime element. The criteria becomes quite simple in…