7 papers
Integral magneticity of the level-two K3 packet: CM theta lifts and a 2-isogeny trace contraction
Alex Shvets
Bönisch, Duhr, and Maggio introduced three meromorphic modular forms \(C_4,C_{6a},C_{6b}\) on \(Î_0(2)\), arising from a hypergeometric K3 family, and conjectured that they are m…
A full supercongruence tower for a level-three symmetric-cube hypergeometric sequence
Alex Shvets
Let . We prove the full prime-power supercongruence tower for , , . The…
Split-prime supercongruence at the mixed CM point (1/6, 1/3; 1)
Alex Shvets
For the mixed CM point (a,b,c) = (1/6, 1/3, 1), define A_n^{mix} := 108^n [z^n] _2F_1(1/6, 1/3; 1; z)^3. For every split prime p >= 7, p == 1 mod 3, and every m >= 1, we prove unco…
Order drop, Hecke descent, and a mod supercongruence for symmetric-cube hypergeometric coefficients
Alex Shvets
We prove that the symmetric-cube coefficients satisfy the supercongruence for every prime and every…
Eta-products, Eichler integrals, and the level-8 Apery limit
Alex Shvets
We give an independent eta-product derivation of the level-8 Apery limit lim B_n^{(8)}/s_n = (7/32) zeta(3), where s_n = sum_{k=0}^n C(n,k)^2 C(2k,n)^2 and B_n^{(8)} is the rationa…
Order-3 pi-formulas, Apery-like kernels, and Clausen functoriality for Conservative Matrix Fields
Alex Shvets
Raz, Shalyt, Leibtag, Kalisch, Weinbaum, Hadad, and Kaminer recently showed that formulas for can be organized by canonical polynomial recurrences and partially unified by a r…