The HUJI-BGU Workshop in Arithmetic meets twice a semester,
alternating locations, starting from the year 5780. All are
welcome.

The workshop is currently organized by Ari Shnidman
(HUJI) and Daniel
Disegni (BGU).

The theme of the day will be L-functions of characters, and the arithmetic significance of their special values.

10.30 - 11.00 Welcome and coffee

11.00 - 11:50 Francesco M. Saettone (BGU),

12.05 - 12.55 Zev Rosengarten (HUJI),

14.15 - 15.05 Amnon Besser (BGU),

16.00 -16.15 (bonus content): Ishai Dan-Cohen (BGU)

Francesco M. Saettone (11.00-11.50)

John Tate in his PhD thesis (Princeton 1950) reproved the functional equation and the analytic continuation of Hecke L-functions. By class field theory, which I will recall, those are L-functions of characters of Galois group. Tate's new proof consists in an innovative use of adelic integration, i.e., Fourier analysis on the adeles: after a quick review of fundamental tools from harmonic analysis, I will introduce the main results of the adelic machinery (adeles and ideles, strong approximation theorem, idele class group) and how they have been used in the study of local and global zeta functions. This approach gives a more conceptually clarifying point of view on Hecke's result (1920).

Zev Rosengarten (12.05-12.55)

The classical class number formula relates the residue of the
zeta function of a number field to the regulator of the group of
units. Similarly, the Birch and Swinnerton-Dyer Conjecture relates
the value of the L-function of an elliptic curve to a "regulator,"
namely the period of the N\'eron differential along a real cycle.
These conjectures found a common generalization in work of
Deligne, and ultimately, Beilinson, who formulated a general
conjecture relating special L-values to regulators of period maps.
We will discuss this conjecture, providing examples along the way,
and then sketch Beilinson's proof of his conjecture for
0-dimensional abelian motives over Q (which is just a fancy way of
saying Dirichlet characters).

Amnon Besser (14.15-15.05)

I will begin by explaining the general philosophy, due to
Perrin-Riou, of p-adic Beilinson conjectures. I will then explain
how one can test this conjecture numerically for totally real
Artin motives using an explicit description of K-theory of fields
and the p-adic polylogarithm.

Yotam Svoray (15.20-16.00)

TBA

Ishai Dan-Cohen (16.00-16.15)

TBA

Yotam Svoray (15.20-16.00)

TBA

Ishai Dan-Cohen (16.00-16.15)

TBA

TBA

Locations

BGU: Deichmann Building for Mathematics (building 58), Ben-Gurion University of the Negev, Be'er Sheva.