142 citations · 752 across the 110 of their papers we have counts for
11 papers · 1 filter
Waring's Theorem for Binary Powers
Daniel M. Kane, Carlo Sanna, Jeffrey Shallit
A natural number is a binary 'th power if its binary representation consists of consecutive identical blocks. We prove an analogue of Waring's theorem for sums of binary …
On the Joint Distribution Of and in Quadratic Twist Families
Daniel Kane, Zev Klagsbrun
If is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\dim_{\mathbb{F}_2}\mathrm{Sel}_ϕ(E^d/\mathbb{Q}) - \…
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves
Manjul Bhargava, Daniel M. Kane, Hendrik W. Lenstra +2
Using maximal isotropic submodules in a quadratic module over Z_p, we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short…
A proof of Andrews' conjecture on Partitions with no short sequences
Daniel M. Kane, Robert C. Rhoades
Holroyd, Liggett, and Romik introduced the following probability model. Let be independent events with probabilities under a probability measur…
On the Number of ABC Solutions with Restricted Radical Sizes
Daniel M. Kane
We consider a variant of the ABC Conjecture, attempting to count the number of solutions to , in relatively prime integers each of absolute value less than wit…
Minimal S-universality criteria may vary in size
Noam D. Elkies, Daniel M. Kane, Scott D. Kominers
In this note, we give simple examples of sets S of quadratic forms that have minimal S-universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh…