Undergraduate Research & Scholarships

Xiaoyu Niu Sciences

Further Computations on Maedas Conjecture

Yoshitaka Maeda made the conjecture in 1997: Let m be an integer greater than 1 and let F be the characteristic polynomial of the Hecke operator T_m acting on the space S_k of cusp forms of weight k and level one, then the polynomial F is irreducible over the field of rational numbers; the Galois group of the splitting field of F is the full symmetric group _d, where d is the dimension of S_k. Most recent computations via Sage have verified the conjecture for k 14000. Xiaoyus project will focus on computing via Sage for k > 14000 and/or considering bigger n than whats currently available. She hopes to either provide more evidence or to find results that disprove the conjecture. She may make theoretical attempts at the conjecture.

Profile image of Xiaoyu Niu
Major: Mathematics
Mentor: Mentor: Sug Woo Shin, Mathematics
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