On \(L\)-functions of ternary zero forms and exponential sums of Lee and Weintraub
type: Item
instance of: scholarly article
title: On \(L\)-functions of ternary zero forms and exponential sums of Lee and Weintraub
zbMATH Open document ID: 0824.11033
author: Tomoyoshi Ibukiyama
author: Hiroshi Saito
published in: Journal of Number Theory
publication date: 1994-09-28T00:00:00Z
review text: \(L\)-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.
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 645297
zbMATH Keywords: \(L\)-functions of ternary zero forms
zbMATH Keywords: special values
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: exponential sum
zbMATH Keywords: trace formula
reviewed by: Masakazu Muro
MaRDI profile type: Publication
full work available at URL: jnth.1994.1066
OpenAlex ID: W1965091945
DOI: 10.1006/JNTH.1994.1066
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description: scientific article; zbMATH DE number 645297