An elementary proof of the Selberg identity for Kloosterman sums

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arxiv 2306.16929 v1 pith:NP35UAWP submitted 2023-06-29 math.NT

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keywords elementaryidentitykloostermanproofselbergsumsadditivecharacters

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We give an elementary proof of the Selberg identity for Kloosterman sums, which only requires the orthogonality of additive characters.

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Triple sums of Kloosterman sums and the discrepancy of modular inverses
math.NT 2024-11 accept novelty 7.0 of 10

For modular inverses with moduli up to X, the paper proves quantitative box, ball, and convex discrepancy bounds, powered by a new triple Kloosterman sum estimate.