6 papers · 1 filter
ABC implies that Ramanujan's tau function misses almost all primes
David Kurniadi Angdinata, Evan Chen, Chris Cummins +21
Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…
Ties in Function Field Prime Races
Graeme Bates, Ryan Jesubalan, Seewoo Lee +2
The function field analogue of Chebyshev's bias was first studied by Cha. In this paper, we study *ties* in this race, namely collections of distinct congruence classes $c_1, \dots…
Almost all primes are partially regular
Evan Chen, Chris Cummins, Ben Eltschig +18
For odd primes , we let be the th cyclotomic field and let denote its Teichmuller character. For , we say that an odd prime is partially…
Powerful Fibonacci polynomials over finite fields
Graeme Bates, Ryan Jesubalan, Seewoo Lee +2
Bugeaud, Mignotte, and Siksek proved that the only perfect powers in Fibonacci sequence are 0, 1, 8, and 144. In this paper, we study the polynomial analogue of the problem. Especi…
Modulation groups
Jayce R. Getz, Armando Gutiérrez Terradillos, Farid Hosseinijafari +6
Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptio…
Shanks' bias in function fields
Seewoo Lee
We study the function field analogue of Shanks bias. For Liouville function , we compare the number of monic polynomials with and for…