About
Welcome to the Reading Group on 𝛆-factors. Unless otherwise announced, all meetings will be held on Thursdays in salle Kampé de Fériet, bâtiment M2.
It is encouraged to read the following introductory handout. It explains the motivation behind the study of ε-factors, provides historical context, and outlines the structure of the reading group.
📄 Read the HandoutSeminar Schedule
| Date & Time | Speaker | Title | Notes |
|---|---|---|---|
| Thu, Sep 11, 2025 — 10:00 | Mladen | Introduction to 𝛆 - factors | |
| Thu, Sep 25, 2025 — 09:30 | Ivan | Local fields and Haar Measure | |
| Thu, Oct 02, 2025 — 09:30 | Xavier | Functional Equation for GL1(F) | |
| Fri, Oct 10, 2025 — 14:00 | Sidonie | Global zeta function | |
| Fri, Oct 17, 2025 — 14:00 | Ilyana | Non-Archimedean Weil Representations I | |
| Thu, Oct 23, 2025 — 09:30 | Sanyam | Non-Archimedean Weil Representations II | |
| Thu, Nov 06, 2025 — 09:30 | Mladen | Weil-Deligne représentations | |
| Thu, Nov 13, 2025 — 09:30 | Cécile | 𝛆-factors for orthogonal representations | |
| Thu, Nov 20, 2025 — 09:30 | Didier | Deligne’s formula and epsilon factors for GL(2) | |
| Thu, Nov 27, 2025 — 09:30 | Arthur | 𝛆-factors for triple product of GL(2) |
Recommended References
Here are some key references related to 𝛆-factors. They are organized by topic, so you can easily find background reading, classical results, and modern treatments.
Foundational Work on Functional Equations
These are Deligne’s seminal papers where he develops the theory of epsilon factors and functional equations of L-functions. Essential for understanding the general framework.
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P. Deligne,
Les constantes des équations fonctionnelles,
in Séminaire Delange-Pisot-Poitou. Théorie des nombres
📄 Read PDF -
P. Deligne,
Les constantes des équations fonctionnelles des fonctions L,
in Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972),
Lecture Notes in Math., Vol. 349, Springer, Berlin-New York, 1973, pp. 501–597.
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Applications to Artin L-Functions and Galois Representations
These works apply the theory to Artin L-functions and study the behavior of root numbers and local constants in concrete settings.
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A. Fröhlich and J. Queyrut,
On the functional equation for the Artin L-function for characters of real representations,
Invent. Math. 20 (1973), pp. 125–138.
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David E. Rohrlich,
Galois theory, elliptic curves, and root numbers,
Compositio Mathematica, Volume 100 (1996), no. 3, pp. 311–349.
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Representation-Theoretic Approaches
This paper provides a representation-theoretic perspective on local epsilon-factors, which is crucial for modern number theory and the study of automorphic forms.
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Dipendra Prasad,
Trilinear forms for representations of GL₂ and local epsilon-factors,
Compositio Mathematica, Volume 75 (1990), no. 1, pp. 1–46.
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