【摘要】 华林-哥德巴赫方程的小素数解问题是堆垒素数论研究领域的重要研究课题,历来备受解析数论学者关注.本文研究一类满足必要条件的不等次幂华林-哥德巴赫方程的小素数解问题.利用标准的Hardy-Littlewood圆法和先进的Davenport方法,结合素变数三角和估计的最新成果及更加有效的H¨older不等式,得到该方程小素数解的更好上界,改进已有的研究结果.更多还原

【Abstract】 The problem of small prime solutions to the Waring-Goldbach type equation is an important research project in the field of additive prime number theory. It has attracted the attention of many analytic number theorists. This topic is to study the problem of small prime solutions to an unlike Waring-Goldbach type equation satisfying some necessary conditions. Using the standard HardyLittlewood cicle method and the advanced Davenport method, combining the latest results of the estimate of the exponential sum over primes and the more efficient H¨older inequalities, then it gets the better upper bound of small prime solutions to this equation and finally the result gives an improvement of the recent result.更多还原