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math.NT2014
Congruences of concave composition functions
Keenan Monks, Lynnelle Ye
Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo of the number of concave compositions. Let $c(n)…
math.NT2014
Congruence properties of Borcherds product exponents
Keenan Monks, Sarah Peluse, Lynnelle Ye
In his striking 1995 paper, Borcherds found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of…
math.NT2014★ 3 cited
Strings of special primes in arithmetic progressions
Keenan Monks, Sarah Peluse, Lynnelle Ye
The Green-Tao Theorem, one of the most celebrated theorems in modern number theory, states that there exist arbitrarily long arithmetic progressions of prime numbers. In a related…