Jared Ruiz

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In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit modular towers. In particular, we give two explicit constructions based on two examples of his formulas and demonstrate that the resulting elements have high order. Between the(More)
In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit modular towers. In particular, we give two explicit constructions based on two examples of his formulas and demonstrate that the resulting elements have high order. Between the(More)
In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit modular towers. In particular, we give two explicit constructions based on two examples of his formulas and demonstrate that the resulting elements have high order. Between the(More)
Let µ be a finite, positive measure on [−1, 1], {Pn} n∈AE the poly-nomials orthonormal with respect to µ and {Snf } n∈AE the associated Fourier series for each function f. The range of p for which Snf converges to f for every f ∈ L p (µ) has been determined only for particular measures. In this paper, we show how to obtain more general results by perturbing(More)
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