L函数在临界带边缘的上界
Upper bounds on L-functions at the edge of the critical strip
摘要：
寻找L函数在临界带边缘的上界的问题有着悠久而有趣的历史。在这里，经典的L函数，如狄利克雷L函数的情况是比较好理解的。其原因是因为已知这些L函数的系数的大小是小的。虽然L函数的系数通常在素数处被常数所限制，但这只在一小部分熟悉的例子中得到了证明。我们的主要重点是在这里的问题，找到上界的L函数，我们有比较坏的界限的大小的系数。
英文摘要：
The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Dirichlet L-functions is relatively well understood. The reason for this is because the size of the coefficients of these L-functions is known to be small. Although L-functions are generally expected to have coefficients which are bounded by a constant at the primes, this has only been proven for a small class of familiar examples. Our main focus here is on the problem of finding upper bounds for L-functions for which we have comparatively bad bounds for the size of the coefficients.
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