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

ISBN: 9780549791447

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97 pages


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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. by Keith J McDonald
| ebook | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 97 pages | ISBN: 9780549791447 | 10.50 Mb

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.



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