An Introduction to the Theory of Local Zeta Functions

By J. Igusa. 2007

333 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/974151eb05dfd91909b9fc77e36e37668593281c

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In Algebra and Number Theory

In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Motivic Serre invariants, ramification, and the analytic Milnor fiber (2007, methodology): “When f is defined over Q, Igusa’s Monodromy Conjecture predicts an intriguing connection between the eigenvalues of the monodromy at complex points of f−1(0) ⊂ Cn, and the poles of Zp(f, s), for almost all primes p, where f is considered as a complex, respectively p-adic polynomial.”
Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B (2011, background): “[25, 21] for further details on PVS, and [12, Section 7] for details on the Bernstein-Sato polynomial conjecture.”
Constructible motivic functions and motivic integration (2004, methodology): “The statement about bianaliticity is well known and follows from the Inverse Function Theorem for complete fields, stated in [26], Corollary 2.”
Constructible exponential functions, motivic Fourier transform and transfer principle (2005, neutral): “[22]) may be restated as follows:”
IMPANGA lecture notes on log canonical thresholds (2011, background): “context of polynomials with real coeﬃ- cients. We have stated this in the complex case, since it then relates to what we will discuss in §1. For a treatment of both the real and the complex case, see [Igu]. AN INTRODUCTION TO LOG CANONICAL THRESHOLDS 3 the so-called Termination of Flips conjecture i”
Zeta functions of groups and rings (2007, background): “The references in [28] provide access to the vast literature on this subject.”