64 citations · 140 across the 23 of their papers we have counts for
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math.NT2011★ 16 cited
Orbital L-functions for the space of binary cubic forms
Takashi Taniguchi, Frank Thorne
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formul…
math.NT2011
Shintani's zeta function is not a finite sum of Euler products
Frank Thorne
We prove that the Shintani zeta function associated to the space of binary cubic forms cannot be written as a finite sum of Euler products. Our proof also extends to several closel…
math.NT2011★ 64 cited
Secondary terms in counting functions for cubic fields
Takashi Taniguchi, Frank Thorne
We prove the existence of secondary terms of order X^{5/6} in the Davenport-Heilbronn theorems on cubic fields and 3-torsion in class groups of quadratic fields. For cubic fields t…