Streamlined WZ Method Proofs of Van Hamme Supercongruences
Streamlined WZ Method Proofs of Van Hamme Supercongruences
Start:
Thursday, March 5, 2026 10:00 am
End:
Thursday, March 5, 2026 12:00 pm
Location:
Valley Library Willamette East
Andres Valloud
Oregon State University
Using the WZ method to prove supercongruences critically depends on an inspired WZ pair choice. This thesis demonstrates a procedure for finding WZ pair candidates to prove a given supercongruence. When suitable WZ pairs are thus obtained, coupling them with the p-adic approximation of Γp by Long and Ramakrishna enables uniform proofs for the Van Hamme supercongruences (B.2), (C.2), (D.2), (E.2), (F.2), (G.2), and (H.2). This approach also yields the known extensions of (G.2) modulo p^4, and of (H.2) modulo p^3 when p is 3 modulo 4. Finally, the Van Hamme supercongruence (I.2) is shown to arise from a special case of the WZ method where Gosper’s algorithm itself succeeds.
Contact:
Carol Murphy