A classical introduction to modern number theory

By K. Ireland, M. Rosen. 1982

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Centers of graded fusion categories (2009, methodology): “very a,b∈ A×, we have X x∈Z/pZ ξax2 = ( a p √ p, if p≡ 1(mod4), a p i √ p, if p≡ 3(mod4) and X (x 1,x 2)∈Z/pZ×Z/pZ ξax2 1−bx 2 2 = ab p p. Proof. The ﬁrst assertion is well known, see for example [R]. The second assertion is an easy consequence of the ﬁrst.CENTERS OF GRADED FUSION CATEGORIES 21 Us”
Hypergeometric Functions over Finite Fields (2015, background): “4 of [44]) which says that the Gauss sum of g(A) over Fq and the Gauss sum g(Ar) over Fqr are related by”
Elementary Number Theory (2008, background): “(For more on higher reciprocity, see [IR90].”
Hypergeometric functions over F_p and relations to elliptic curves and modular forms (2008, methodology): “Using known formulas for a(E) in the case of curves with j-invariant 1728 (see Chapter 18 of [10]), one can show that a(E) = ±2a,±2b for all E appearing in (9).”