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Counting integer polynomials with several roots of maximal modulus
Artūras Dubickas, Min Sha
In this paper, for positive integers and , we obtain some estimates on the cardinality of the set of monic integer polynomials of degree and height bounded by …
Möbius Randomness Law for Frobenius Traces
Min Sha, Igor E. Shparlinski
Recently E. Bombieri and N. M. Katz (2010) have demonstrated that several well-known results about the distribution of values of linear recurrence sequences lead to interesting sta…
A proof of Sondow's conjecture on the Smarandache function
Xiumei Li, Min Sha
The Smarandache function of a positive integer , denoted by , is defined to be the smallest positive integer such that divides the factorial . In this note, we…
Polynomial analogue of the Smarandache function
Xiumei Li, Min Sha
In the integer case, the Smarandache function of a positive integer is defined to be the smallest positive integer such that divides the factorial . In this paper,…
Torsion points with multiplicatively dependent coordinates on elliptic curves
Fabrizio Barroero, Min Sha
In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove th…
Primes in arithmetic progressions and nonprimitive roots
Pieter Moree, Min Sha
Let be a prime. If an integer generates a subgroup of index in then we say that is a -near primitive root modulo . We point out th…