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Abstracts for PLeaSANT (Participative Learning Seminar on Any Number Theory)

Alternatively have a look at the program.

Jacobi forms and Kaneko--Zagier type equations

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Speaker: 
Dmitrii Adler
Zugehörigkeit: 
MPIM
Datum: 
Die, 22/04/2025 - 16:30 - 17:30
Location: 
MPIM Lecture Hall

For modular forms, the Kaneko--Zagier equation is a second-order differential equation with respect to the Serre derivative. Analogously, for Jacobi forms, there exists an analogue of the Serre derivative that increases the weight of a Jacobi form by 2 and preserves its index. It is not difficult to describe the kernel of this operator, but finding solutions of even second-order differential equations, known as Kaneko--Zagier type equations, is not such a trivial problem. In my talk, I will present some current progress on this topic.

 

Density questions on primitive divisors of Lucas sequences

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Speaker: 
Joaquim Cera Da Conceicao
Zugehörigkeit: 
Université de Caen/MPIM
Datum: 
Mon, 28/04/2025 - 16:30 - 17:30
Location: 
MPIM Lecture Hall

It is known that every term $U_n$ of a regular Lucas sequence has a primitive prime divisor if $n\ge 31$, i.e., a prime $p$ such that $p\mid U_n$ but $p\nmid U_k$, for all $1\leq k<n$. Can this be refined to specific sets of primes?

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