scholarly journals Computing Igusa’s local zeta function of univariates in deterministic polynomial-time

2020 ◽  
Vol 4 (1) ◽  
pp. 197-214
Author(s):  
Ashish Dwivedi ◽  
Nitin Saxena
Keyword(s):  
Zeta Function ◽  
Polynomial Time ◽  
Local Zeta Function

scholarly journals A new generating function for calculating the Igusa local zeta function

2017 ◽  
Vol 304 ◽  
pp. 355-420 ◽  
Author(s):  
Raemeon A. Cowan ◽  
Daniel J. Katz ◽  
Lauren M. White
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Local Zeta Function

scholarly journals Poles of the Igusa local zeta function of some hybrid polynomials

2014 ◽  
Vol 25 ◽  
pp. 37-48
Author(s):  
Edwin León-Cardenal ◽  
Denis Ibadula ◽  
Dirk Segers
Keyword(s):  
Zeta Function ◽  
Local Zeta Function

scholarly journals The local zeta function for symmetric spaces of non-compact type

2011 ◽  
Vol 61 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Tomás F. Godoy ◽  
Roberto J. Miatello ◽  
Floyd L. Williams
Keyword(s):  
Zeta Function ◽  
Symmetric Spaces ◽  
Compact Type ◽  
Local Zeta Function

The zeta function of [sfr ][lfr ]2 and resolution of singularities

2002 ◽  
Vol 132 (1) ◽  
pp. 57-73 ◽  
Author(s):  
MARCUS DU SAUTOY ◽  
GARETH TAYLOR
Keyword(s):  
Zeta Function ◽  
Finite Index ◽  
General Result ◽  
Quantifier Elimination ◽  
Rational Functions ◽  
Resolution Of Singularities ◽  
Euler Product ◽  
Product Decomposition ◽  
Local Factors ◽  
Local Zeta Function

Let L be a ring additively isomorphic to ℤd. The zeta function of L is defined to bewhere the sum is taken over all subalgebras H of finite index in L. This zeta function has a natural Euler product decomposition:These functions were introduced in a paper of Grunewald, Segal and Smith [5] where the local factors ζL[otimes ]ℤp(s) were shown to always be rational functions in p−s. The proof depends on representing the local zeta function as a definable p-adic integral and then appealing to a general result of Denef’s [1] about the rationality of such integrals. The proof of Denef relies on Macintyre’s Quantifier Elimination for ℚp [8] followed by techniques developed by Igusa [6] which employ resolution of singularities.

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