Glossary

This glossary collects the terms and symbols that a new reader is most likely to need while moving between the compact note, the monograph, and the core concept pages.

Core Objects

Term	Meaning	Primary page
`MTMN`	The multiplication table modulo $N$ on the window $1 \le x,y \le N-1$.	MTMN
`A_{N,a}`	The lattice points with product congruent to residue $a$ modulo $N$.	A_N_a
`S(N,a)`	Area of the convex hull of $A_{N,a}$.	S_N_a
`S(N)`	Total area sum $\sum_a S(N,a)$.	S_N
`modular hyperbola`	Standard literature name for a single congruence class $xy \equiv a \pmod N$.	modular_hyperbolas

Zero-Class Terms

Term	Meaning	Primary page
`zero class`	The residue class $A_{N,0}$.	zero_class_geometry
`divisor rectangle`	The rectangle $R_d=[d,N-d]\times[N/d,N-N/d]$ attached to a proper divisor $d$ of $N$.	zero_class_geometry
`divisor points`	The sampled points $(d,N/d)$ and $(N-d,N/d)$ controlling the lower hull of the zero class.	zero_class_geometry
`\ell_N(x)`	The lower broken-line envelope coming from the divisor-point hull.	zero_class_geometry
`\Delta_N`	The hyperbola-gap correction between the divisor envelope and $y=N/x$ on the informative half.	zero_class_hyperbola_gap

Boundary-Model Terms

Term	Meaning	Primary page
`B^{(1)}_{N,a}`	First boundary points: rows and columns $1$ and $N-1$.	first_boundary_model
`S^{(1)}(N,a)`	Area of the first-boundary hull.	first_boundary_model
`B^{(2)}_{N,a}`	Second boundary points: rows and columns $2$ and $N-2$.	second_boundary_model
`S^{(2)}(N,a)`	Area of the second-boundary hull.	second_boundary_model

Supporting Terms

Term	Meaning	Primary page
`support function`	The direction-wise extremal function of a convex hull.	S_N_a

Background

If you want a slower route before returning to the theorem pages, go next to: