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Number Theory Seminar

Title: Linear congruence relations for exponents of Borcherds products
Speaker: Badri Vishal Pandey (University of Cologne, Germany)
Date: 01 March 2024
Time: 10 am
Venue: LH-1

For all positive powers of primes $p \geq 5$, we prove the existence of infinitely many linear congruences between the exponents of twisted Borcherds products arising from a suitable scalar-valued weight $1/2$ weakly holomorphic modular form or a suitable vector-valued harmonic Maassform. To this end, we work with the logarithmic derivatives of these twisted Borcherds products, and offer various numerical examples of non-trivial linear congruences between them modulo $p=11$. In the case of positive powers of primes $p = 2, 3$, we obtain similar results by multiplying the logarithmic derivative with a Hilbert class polynomial as well as a power of the modular discriminant function. Both results confirm a speculation by Ono. (joint work with Andreas Mono).


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 20 Apr 2024