Lecture Room B, 4th Floor, The 3rd General Building , NTHU + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 清大綜合三館Lecture Room B+ Cisco WebEx)
A Generalization of Pellarin's Identity to Drinfeld Modules of Arbitrary Rank
Giacomo Hermes Ferraro (Sapienza Università di Roma)
Abstract
The Anderson–Thakur special function is a key object in the study of the Carlitz module and its tensor powers. Pellarin proved that its product with a zeta-like series yields a rational function over a base change of the projective line, a result later generalized by Green and Papanikolas to Drinfeld modules of rank 1 over an elliptic curve.
In the setting of arbitrary Drinfeld modules over a curve X of any genus, I introduce two functors whose universal objects naturally generalize both the Anderson–Thakur special function and the Pellarin zeta function.
I show how to define a scalar product of these two objects (and their frobenius twists), obtaining a family of rational differential forms over a base change of X, indexed by the integers. Finally, I provide a characterization of the generating series associated with these scalar products.
Meeting number (access code): 2515 073 2781
Meeting password: R7f3dirpmq7
Organizers: Fu-Tsun Wei (NTHU)
