American Journal of Mathematics, Vol. 141, No. 4 (August 2019), pp. 907-940 (34 pages) Let 𝑝 be an odd prime. We show that the compositum of the Hecke field of a normalized Hecke eigen cuspform for ...

Algebraic geometry, the study of solutions to polynomial equations and their geometric properties, finds rich interplay with class field theory—a branch of number theory that classifies abelian ...

An algorithm for realizing finite field arithmetic is presented. The relationship between linear recursions and polynomial arithmetic (modulo a fixed polynomial) over ...

One of my fellow contributors here recently wrote a post about leap years and why we have them. This reminded me of modular arithmetic and the formula for calculating the day of the week for any date ...

I'm sure FPGA logic designers have often heard it said: “We just need to take this number mod 3.” Or maybe something like, “Just round to the nearest hundred.” This latter case really means: “Take the ...