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On Character Sums of Binary Quadratic Forms 1 2 Mei-Chu Chang3

On Character Sums of Binary Quadratic Forms 1 2 Mei-Chu Chang3 2025

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The document discusses character sum bounds for binary quadratic forms, specifically focusing on the character sum of the form χ(x² + ky²) where χ is a nontrivial character modulo a large prime p. It establishes upper bounds for these sums under certain conditions and provides applications, including proving that x² + k is a quadratic non-residue modulo p for some x in a specified range. The results build upon previous work by Burgess and extend the understanding of character sums in number theory.

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