In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further result...In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi.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
Let E（X）=[{N≤X;N≠p<sub>1</sub><sup>2</sup>+p<sub>2</sub><sup>3</sup>+p<sub>3</sub><sup>4</sup>+p<sub>4</sub><sup>5</sup&...Let E（X）=[{N≤X;N≠p<sub>1</sub><sup>2</sup>+p<sub>2</sub><sup>3</sup>+p<sub>3</sub><sup>4</sup>+p<sub>4</sub><sup>5</sup> for any primes p<sub>i</sub>}|.It is proved in this paper that there exists a positive constant δ】0 such that E（X）《<sub>δ</sub>X<sup>1-δ</sup> which improves a result of prachar.展开更多
基金supported by the National Natural Science Foundation of China (11171119,11126145,11026096)the Nature Science Foundation of Jiangxi Province in China(20114BAB211003)
文摘In this article, we consider some type of q-difference equations, which have meromorphic solutions with Borel exceptional zeros and poles. We also give a precise result in the finite order case and some further results in a particular case where qi = qi.
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.
文摘Let E（X）=[{N≤X;N≠p<sub>1</sub><sup>2</sup>+p<sub>2</sub><sup>3</sup>+p<sub>3</sub><sup>4</sup>+p<sub>4</sub><sup>5</sup> for any primes p<sub>i</sub>}|.It is proved in this paper that there exists a positive constant δ】0 such that E（X）《<sub>δ</sub>X<sup>1-δ</sup> which improves a result of prachar.
