Let \(F\) be a p-adic field, let \(\psi \) be a non-trivial character of F, and let \(\chi \) be a character of \(F^*\). In this short note we present two new identities involving \(\gamma (s,\chi ,\psi )\), \(\gamma (\psi )\), and \(\widetilde{\gamma }(s,\chi ,\psi )\) along with a duplication formula for \(\gamma (s,\chi ,\psi )\). Here \({\gamma }(s,\chi ,\psi )\) is the Tate \(\gamma \)-factor, \(\gamma (\psi )\) is the Weil index, and \(\widetilde{\gamma }(s,\chi ,\psi )\) is the metaplectic \(\widetilde{\gamma }\)-factor. As a result we give a new proof for a useful identity involving these three factors originally proven by W. Jay Sweet.

令\（F \）为p -adic字段，令\（\ psi \）为F的平凡字符，令\（\ chi \）为\（F ^ * \）的字符。在此简短说明中，我们介绍了两个新的身份，包括\（\ gamma（s，\ chi，\ psi）\），\（\ gamma（\ psi）\）和\（\ widetilde {\ gamma}（s，\ chi，\ psi）\）以及\（\ gamma（s，\ chi，\ psi）\）的复制公式。这里\（{\ gamma}（s，\ chi，\ psi）\）是Tate \（\ gamma \）- factor，\（\ gamma（\ psi）\）是Weil索引，而\（\ widetilde {\ gamma}（s，\ chi，\ psi）\）是元整数\（\ widetilde {\ gamma} \）-因子。结果，我们为涉及W.Jay Sweet最初证明的这三个因素的有用身份提供了新的证据。