17 citations · 93 across the 37 of their papers we have counts for
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math.NT2009★ 14 cited
Common values of the arithmetic functions phi and sigma
Kevin Ford, Florian Luca, Carl Pomerance
We show that the equation phi(a)=σ(b) has infinitely many solutions, where phi is Euler's totient function and sigma is the sum-of-divisors function. This proves a 50-year old conj…
math.NT2009★ 1 cited
Rank statistics for a family of elliptic curves over a function field
Carl Pomerance, Igor E. Shparlinski
We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter . This is perhaps…