A note on the zeros of zeta and L-functions

作者：Carneiro Emanuel; Chandee Vorrapan^*; Milinovich Micah B

来源：Mathematische Zeitschrift, 2015, 281(1-2): 315-332.

DOI：10.1007/s00209-015-1485-9

• Riemann zeta-function
• Automorphic L-functions
• Beurling-Selberg extremal problem
• Extremal functions
• Exponential type

Let denote the argument of the Riemann zeta-function at the point . Assuming the Riemann hypothesis, we give a new and simple proof of the sharpest known bound for S(t). We discuss a generalization of this bound for a large class of L-functions including those which arise from cuspidal automorphic representations of GL(m) over a number field. We also prove a number of related results including bounding the order of vanishing of an L-function at the central point and bounding the height of the lowest zero of an L-function.

• 出版日期2015-10