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Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
Motivic zeta functions degenerations of abelian varieties Calabi-Yau varieties
2011/2/25
Let f ∈ Z[x1, . . . , xn] be a non-constant polynomial, and let p be a prime. Igusa’s p-adic zeta function Zp f (s) is a meromorphic function on the complex plane that encodes the number of solutions ...
Zeta functions and Bernstein-Sato polynomials for ideals in dimension two
Zeta functions Bernstein-Sato polynomials ideals dimension two
2011/2/28
For a nonzero ideal I ⊳C[x1, . . . , xn], with 0 ∈ supp I, a (general-ized) conjecture of Igusa–Denef–Loeser predicts that every pole of its topologi-cal zeta function is a root of its Bernstein...
On the zeros of Weng zeta functions for Chevalley groups
Weng zeta functions Chevalley groups
2010/11/23
We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over $\Q$ are simple and on the critical line.
Functional equations for Weng's zeta functions for $(G,P)/\mathbb{Q}$
Functional equations Weng's zeta functions
2010/11/23
It is shown that Weng's zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equatio...
Milnor-Selberg zeta functions and zeta regularizations
Milnor-Selberg zeta functions zeta regularizations
2010/11/19
By a similar idea for constructing Milnor's gamma functions, we study ``higher depth determinants'' of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a general...
Computing special values of partial zeta functions
Computing special values partial zeta functions
2010/10/29
We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the \emph{Eisenstein cocycle} $\Psi $, a group cocycle for $GL_{n} (\Z...