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math.NT2010★ 37 cited
On the number of summands in Zeckendorf decompositions
Murat Kologlu, Gene Kopp, Steven J. Miller +1
Zeckendorf proved that every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers. Once this has been shown, it's natural to ask how many summ…
math.NT2010★ 9 cited
Effective equidistribution and the Sato-Tate law for families of elliptic curves
Steven J. Miller, M. Ram Murty
Extending recent work of others, we provide effective bounds on the family of all elliptic curves and one-parameter families of elliptic curves modulo p (for p prime tending to inf…
math.NT2010
Low-lying Zeros of Number Field -functions
Steven J. Miller, Ryan Peckner
One of the most important statistics in studying the zeros of L-functions is the 1-level density, which measures the concentration of zeros near the central point. Fouvry and Iwani…