We prove an identity which lifts a hyper-Kloosterman sum to an exponential sum over a quadratic extension field. The identity matches two Shalika germs of a relative trace formula for GL(n) which might be used to characterize the image of quadratic base change for GL(n).
On Two Exponential Sums and Their Applications
β Scribed by Han Wen Bao
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 275 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1071-5797
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β¦ Synopsis
We give estimates of two exponential sums over finite fields for which Weil's estimates fail. Using our estimates and Cohen's sieve method, we prove the conjecture of Hansen and Mullen for the second coefficient in characteristic two when the degree Υ7.
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