In Ref. [1] Mautner established an identity in a finite form between a p-adic spherical function on GL(2) and its Satake transform. This identity was generalized by the author to GL(3) in Ref. [2]. On the other hand, ...In Ref. [1] Mautner established an identity in a finite form between a p-adic spherical function on GL(2) and its Satake transform. This identity was generalized by the author to GL(3) in Ref. [2]. On the other hand, the author proved in Ref. [3] an identity in a similar finite form expressing the Whittaker transform of a p-adic spheri-展开更多
1 Local Orbital Integrals In Ref. [1] Jacquet and Ye conjectured a relative trace formula for GL(n) which could be used to show that an automorphic representation π of GL(n) over a number field is a quadratic base ch...1 Local Orbital Integrals In Ref. [1] Jacquet and Ye conjectured a relative trace formula for GL(n) which could be used to show that an automorphic representation π of GL(n) over a number field is a quadratic base change if and only if it is distinguished, a theorem first proved by Harder, Langlands and Rapoport for GL(2). This property of π being distinguished then might imply a possible pole of an L-function attached to the representation π. For GL(2)展开更多
From a Davenport\|Hasse identity of Gauss sums an identity of a hyper\|Kloosterman sum has been deduced. Using this identity the theory of Kloosterman sheaves and equidistribution of hyper\|Kloosterman sums can be app...From a Davenport\|Hasse identity of Gauss sums an identity of a hyper\|Kloosterman sum has been deduced. Using this identity the theory of Kloosterman sheaves and equidistribution of hyper\|Kloosterman sums can be applied to an exponential sum over a cyclic algebraic number field of prime degree. This identity might also be applied to base change problems in representation theory via a possible relative trace formula over the cyclic number field.展开更多
文摘In Ref. [1] Mautner established an identity in a finite form between a p-adic spherical function on GL(2) and its Satake transform. This identity was generalized by the author to GL(3) in Ref. [2]. On the other hand, the author proved in Ref. [3] an identity in a similar finite form expressing the Whittaker transform of a p-adic spheri-
基金Porject supported in part by NSF (USA) grant # DMS 9003213
文摘1 Local Orbital Integrals In Ref. [1] Jacquet and Ye conjectured a relative trace formula for GL(n) which could be used to show that an automorphic representation π of GL(n) over a number field is a quadratic base change if and only if it is distinguished, a theorem first proved by Harder, Langlands and Rapoport for GL(2). This property of π being distinguished then might imply a possible pole of an L-function attached to the representation π. For GL(2)
文摘From a Davenport\|Hasse identity of Gauss sums an identity of a hyper\|Kloosterman sum has been deduced. Using this identity the theory of Kloosterman sheaves and equidistribution of hyper\|Kloosterman sums can be applied to an exponential sum over a cyclic algebraic number field of prime degree. This identity might also be applied to base change problems in representation theory via a possible relative trace formula over the cyclic number field.
