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Im, Bo-Hae; Larsen, Michael (, Abelian varieties and number theory)Jarden, Moshe; Shaska, Tony (Ed.)This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry.more » « less
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Im, Bo-Hae; Larsen, Michael (, Abelian varieties and number theory)Jarden, Moshe; Shaska, Tony (Ed.)
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Im, Bo-Hae; Larsen, Michael (, The quarterly journal of mathematics)Let f∈ℚ(x) be a non-constant rational function. We consider ‘Waring’s problem for f(x), i.e., whether every element of ℚ can be written as a bounded sum of elements of {f(a)∣a∈ℚ}. For rational functions of degree 2, we give necessary and sufficient conditions. For higher degrees, we prove that every polynomial of odd degree and every odd Laurent polynomial satisfies Waring’s problem. We also consider the 'easier Waring’s problem': whether every element of ℚ can be represented as a bounded sum of elements of {±f(a)∣a∈ℚ}. .more » « less
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