Abstract. This paper shows that a certain type of Soto-Andrade sum can be estimatedinanelementarywaywhichdoesnotusetheRiemannhypothesis for curves over finite fields and which slightly sharpens previous estimates for this type of Soto-Andrade sum. As an application, we discuss how this implies that certain graphs arising from finite upper half planes in odd characteristic are Ramanujan without using the Riemann hypothesis. 1
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