6 papers
Universality for cokernels of partially random integral matrices
Isaac Rajagopal
Given any , let be a random matrix over , with all entries independent and -balanced (lying in each residue clas…
The discrete logarithm problem in cokernels of -matrices
Isaac Rajagopal
In 2009 and 2010, Blackburn and Shokrieh independently found that the discrete logarithm can be computed efficiently on the sandpile group of a graph, meaning that sandpile groups…
Uniform bounds on periodic points of polynomials with good reduction
Isaac Rajagopal, Robin Zhang
We establish effective bounds on the number of periodic points of degree- polynomials defined over -adic fields and number fields, under a mild reduction hypothesis that…
Possible Sizes of Sumsets
Isaac Rajagopal
Nathanson introduced the range of cardinalities of -fold sumsets Following a remark of Erdős and Szemerédi that de…
Variations on five-dimensional sphere packings
Henry Cohn, Isaac Rajagopal
We analyze Szöllősi's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We co…
The Proportion of Irreducible p-adic Polynomials
Isaac Rajagopal
We attempt to quantify the exact proportion of monic -adic polynomials of degree which are irreducible. We find an exact answer to this when is prime and , and…