Bounds on fewnomial exponential sums over Z p

• Autores: Todd Cochrane, Christopher Pinner
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 149, Nº 2, 2010, págs. 217-227
• Idioma: inglés
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• Resumen

  • We obtain a number of new bounds for exponential sums of the type S(?, f) = ?x = 1p-1 ?(x) ep(f(x)), with p a prime, f(x) = ?i = 1r aixki, ai, ki ? Z, 1 = i = r and ? a multiplicative character (mod p). The bounds refine earlier Mordell-type estimates and are particularly effective for polynomials in which a certain number of the ki have a large gcd with p - 1. For instance, if f(x) = ?i = 1m aixki + g(xd) with d|(p - 1) then . If f(x) = axk + h(xd) with d|(p - 1) and (k, p - 1) = 1 then , and if f(x) = axk + bx-k + h(xd) with d|(p - 1) and (k, p - 1) = 1 then .