4 citations · 6 across the 14 of their papers we have counts for
16 papers
Reciprocal LCM powers and Robin's criterion
Grant Molnar
For , we study the reciprocal LCM-power function \[ σ^{[κ]}_{-1}(n) := \sum_{d \mid n}μ(d)\,σ_{-1}(n / d)^κ. \] We determine its average and extremal orders. A natural Robin-…
Reliability Theory for AI Control
Grant Molnar
Reliability theory gives a mature language for layered systems, but its formal tools are not yet standard in frontier AI control. We apply them to Google DeepMind's defenses agains…
The Tropical Algebra of Binary-Tree Height
Grant Molnar
The binary-tree height recursion defines an algebra on , with join given by and product \[ a\star b=\max\{a,b\}+1. \] We show that w…
The Gregory function and its completed Gregory transform
Grant Molnar
We study the entire interpolation \[ \mathcal{G}(z)=\int_0^1 \binom{x}{z}\,dx \] of the Gregory coefficients. Its completion satisfies the positive Markov-transform identity \[ \fr…
Integral-Differential Calculus
Grant Molnar
We give an exposition of the Newton-Leibniz calculus. We begin by defining the integral as a limit of Riemann sums, verify the integrals of the standard catalog of functions by dir…
On the symmetry of evidential support
Grant Molnar
For events and , we have \[ \mathbb{P}(A\mid B) > \mathbb{P}(A\mid \neg B) \qquad\Longleftrightarrow\qquad \mathbb{P}(B\mid A) > \mathbb{P}(B\mid \neg A) \] whenever all fou…
Reactive means in the Iterated Prisoner's Dilemma
Grant Molnar, Caroline Hammond, Feng Fu
The Iterated Prisoner's Dilemma (IPD) is a well studied framework for understanding direct reciprocity and cooperation in pairwise encounters. However, measuring the morality of va…
A database of basic numerical invariants of Hilbert modular surfaces
Eran Assaf, Angelica Babei, Ben Breen +8
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
Counting elliptic curves over the rationals with a 7-isogeny
Grant Molnar, John Voight
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof, that admit a cyclic isogeny of…
Multiplicative summations into algebraically closed fields
Robert J. MacG. Dawson, Grant Molnar
In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-de…
Telescopic, Multiplicative, and Rational Extensions of Summations
Robert Dawson, Grant Molnar
A summation is a shift-invariant -module homomorphism from a submodule of to or another ring. [11] formalized a method for extending a summation t…
Fast-growing series are transcendental
Robert Dawson, Grant Molnar
Let be a subring of , and let . The Newton-Puiseux Theorem implies that if the coefficients of grow sufficiently rapidly relative to…
The arithmetic of modular grids
Michael Griffin, Paul Jenkins, Grant Molnar
A modular grid is a pair of sequences and of weakly holomorphic modular forms such that for almost all and , the coefficient of in is the neg…
Zagier duality for level weakly holomorphic modular forms
Paul Jenkins, Grant Molnar
We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level with with poles on…
A Savage-Like Axiomatization for Nonstandard Expected Utility
Grant Molnar
Since Leonard Savage's epoch-making "Foundations of Statistics", Subjective Expected Utility Theory has been the presumptive model for decision-making. Savage provided an act-based…
Graphs with the strong Havel-Hakimi property
Michael D. Barrus, Grant Molnar
The Havel-Hakimi algorithm iteratively reduces the degree sequence of a graph to a list of zeroes. As shown by Favaron, Mahéo, and Saclé, the number of zeroes produced, known as th…