Home » On p-adic zeta functions and their derivatives at s = 0. by Keith J McDonald
On p-adic zeta functions and their derivatives at s = 0. Keith J McDonald

On p-adic zeta functions and their derivatives at s = 0.

Keith J McDonald

Published
ISBN : 9780549791447
ebook
97 pages
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 About the Book 

We study the p-adic interpolation of the special values (suitably regularized) of the Shintani cone zeta functions---the building blocks of standard zeta and L-functions---associated to a real quadratic number field F. Our main result is a polynomialMoreWe study the p-adic interpolation of the special values (suitably regularized) of the Shintani cone zeta functions---the building blocks of standard zeta and L-functions---associated to a real quadratic number field F. Our main result is a polynomial time algorithm to calculate the derivative of these functions of the p-adic variable s at s = 0 to high p-adic accuracy. These derivatives are of great interest in view of the classical conjectures of Gross and Stark which express these derivatives at s = 0 in terms of certain units in abelian extensions of F.