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6 papers · 1 filter
Specialization of linear systems from curves to graphs
Matthew Baker
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of…
A lower bound for average values of dynamical Green's functions
Matthew Baker
We provide a Mahler/Elkies-style lower bound for the average values of dynamical Green's functions on the projective line over an arbitrary valued field, and give some dynamical an…
Almost all palindromes are composite
William D. Banks, Derrick N. Hart, Mayumi Sakata
We study the distribution of palindromic numbers (with respect to a fixed base ) over certain congruence classes, and we derive a nontrivial upper bound for the number of p…
Complexity of Inverting the Euler Function
Scott Contini, Ernie Croot, Igor Shparlinski
We present an algorithm to invert the Euler function . The algorithm, for a given , in polynomial time ``on average'', finds the set of all solutions to…
Long Arithmetic Progressions in Critical Sets
Ernie Croot
In this paper we prove: If 0 < d < 1, and p is a sufficiently large prime, then if S is a subset of Z/pZ having the least number of three-term arithmetic progressions among all sub…
On Thin Sets of Primes Expressible as Sumsets
Ernie Croot, Christian Elsholtz
Suppose that P is an infinite set of primes such that P = A + B + C, where A,B,C are sets with at least two elements. We show that if P(x) > c x/log^d x (where P(x) = the number of…