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math.NT2026
Prime detecting quasi-modular forms in higher level
Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau
In a previous work, the authors resolved a conjecture about the structure of prime-detecting quasi-modular forms by studying sign changes occurring in quasi-modular cusp forms. In…
math.NT2025
On a conjecture about prime-detecting quasimodular forms
Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau
Motivated by weighted partition of that vanish if and only if is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes…
math.NT2024
Sums of generalized polygonal numbers of almost prime "length"
Soumyarup Banerjee, Ben Kane, Daejun Kim
In this paper, we consider sums of three generalized -gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions o…