Conditional expanding bounds for two-variable functions over finite valuation rings
نویسندگان
چکیده
In this paper, we use methods from spectral graph theory to obtain some results on the sum-product problem over finite valuation rings R of order qr which generalize recent results given by Hegyvári and Hennecart (2013). More precisely, we prove that, for related pairs of two-variable functions f(x, y) and g(x, y), if A and B are two sets in R∗ with |A| = |B| = qα, then max {|f(A,B)|, |g(A,B)|} |A|,
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 60 شماره
صفحات -
تاریخ انتشار 2017