On \(L\)-functions of ternary zero forms and exponential sums of Lee and Weintraub
\(L\)-functions of ternary zero forms, which are a modification of the zeta functions associated with the prehomogeneous vector space of \(2\times 2\) symmetric matrices acting on by the group \(GL_ 2\), are studied. The special values of such \(L\)-functions are explicitly described in terms of general Bernoulli numbers by discovering remarkable relations between the \(L\)-functions of ternary zero forms and the Riemann zeta function. In addition, they give a proof of a formula for some exponential sum related to the trace formula which was conjectured by Lee and Weintraub.
scientific article; zbMATH DE number 645297
scientific article