This paper develops the study by analytic methods of the generalized principal series Maass forms on GL(3). These forms occur as an infinite sequence of one-parameter families in the two-parameter spectrum of GL(3) Maass forms, analogous to the relationship between the holomorphic modular forms and the spherical Maass cusp forms on GL(2). We develop a Kuznetsov trace formula attached to these forms at each weight and use it to prove an arithmetically-weighted Weyl law, demonstrating the existence of forms which are not self-dual. Previously, the only full level, generalized principal series forms that were known to exist on GL(3) were the self-dual forms arising from symmetric-squares of GL(2) forms. The Kuznetsov formula developed here should take the place of the GL(2) Petersson trace formula for theorems “in the weight aspect”. As before, the construction involves evaluating the Archimedian local zeta integral for the Rankin–Selberg convolution and proving a form of Kontorovich–Lebedev inversion.

本文通过分析方法对GL（3）上的广义主序列Maass形式进行了研究。这些形式以GL（3）Maass形式的两参数谱中的一参数族的无限序列出现，类似于GL（2）上的全纯模态形式和球形Maass尖点形式之间的关系。我们开发了在每种权重下都附加到这些形式的库兹涅佐夫迹线公式，并用它证明了算术加权的韦尔定律，证明了存在非自对偶形式。以前，被知道上存在的唯一满级，全局主系列形式GL（3）来自对称平方所产生的自对偶形式GL（2）表格。这里开发的库兹涅佐夫公式应该代替定理“在重量方面”的GL（2）Petersson跟踪公式。和以前一样，构造过程包括评估Rankin-Selberg卷积的Archimedian局部zeta积分，并证明Kontorovich-Lebedev反演的一种形式。