6 papers · 1 filter
Zeros of Hecke polynomials arising from weak eigenforms
Kevin Gomez
We attach Hecke polynomials to weak Hecke eigenforms of weight and show that, for large , every zero is simple and lies in . The construction pull…
MacMahonesque partition functions detect sets related to primes
Kevin Gomez
Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generaliz…
The second shifted difference of partitions and its applications
Kevin Gomez, Joshua Males, Larry Rolen
A number of recent papers have estimated ratios of the partition function , which appears in many applications. Here, we prove an easy-to-use effective bound on these…
Infinite families of crank functions, Stanton-type conjectures, and unimodality
Kathrin Bringmann, Kevin Gomez, Larry Rolen +1
Dyson's rank function and the Andrews--Garvan crank function famously give combinatorial witnesses for Ramanujan's partition function congruences modulo 5, 7, and 11. While these f…
Supersingular Loci from Traces of Hecke Operators
Kevin Gomez, Kaya Lakein, Anne Larsen
A classical observation of Deligne shows that, for any prime , the divisor polynomial of the Eisenstein series mod is closely related to the supersingula…
Bounds for Coefficients of the Mock Theta Function and Applications to Partition Ranks
Kevin Gomez, Eric Zhu
We compute effective bounds for , the Fourier coefficients of Ramunujan's mock theta function utilizing a finite algebraic formula due to Bruinier and Schwagenscheidt.…