论文标题
带有两个piatetski-shapiro Prime的三元戈德巴赫问题和一个数字缺失的素数
The ternary Goldbach problem with two Piatetski-Shapiro primes and a prime with a missing digit
论文作者
论文摘要
令$γ^*= \ frac {8} {9}+\ frac {2} {3} {\ frac {\ frac {\ log（10/9）} {\ log 10} \ \：（\ by：（\ ldots） 固定的。还让$ a_0 \ in \ {0,1，\ ldots，9 \} $。\\我们证明，我们可以假设一个普遍的Riemann假设，即每个足够大的奇数整数$ n_0 $都可以用$ $ n_0 = p_1+p_1+p_1+p_2+p_2+p_3 \： $ p_i = [n_i^{c_0}] $，$ n_i \ in \ mathbb {n} $，对于$ i = 1,2 $，$ p_3 $的小数扩展不包含数字$ a_0 $。 Piatetski-Shapiro Primes和两个变量中的Hardy-Little Wood Circle方法。这是三元戈德巴赫问题的第一个结果，即混合类型的素数，涉及数字缺失的素数。
Let $$γ^*=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:.$$ Let $γ^*<γ_0\leq 1$, $c_0=1/γ_0$ be fixed. Let also $a_0\in\{0,1,\ldots, 9\}$.\\ We prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer $N_0$ can be represented in the form $$N_0=p_1+p_2+p_3\:,$$ where the $p_i$ are of the form $p_i=[n_i^{c_0}]$, $n_i\in\mathbb{N}$, for $i=1,2$ and the decimal expansion of $p_3$ does not contain the digit $a_0$.\\ The proof merges methods of J. Maynard from his paper on the infinitude of primes with restricted digits, results of A. Balog and J. Friedlander on Piatetski-Shapiro primes and the Hardy-Littlewood circle method in two variables. This is the first result on the ternary Goldbach problem with primes of mixed type which involves primes with missing digits.
