The largest gap between zeros of entire L-functions is less than 41.54

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• 作者：Patrick Kü ; hn^a ; ^{patrick.kuehn@math.uzh.ch} ; Nicolas Robles^b ; ^{nirobles@illinois.edu} ; Alexandru Zaharescu^b ; ^c ; ^{zaharesc@illinois.edu}
• 关键词：Weil explicit formula ; Selberg minorant ; Beurling function ; Largest gap between zeros of L-functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1286-1301
• 全文大小：621 K
• 卷排序：449

文摘

Using suitable feasible pairs and convex combinations of Selberg minorant functions, the upper bound under GRH and the Ramanujan hypothesis on the largest gap between consecutive zeros of an entire L-function in Bober, Conrey, Farmer, Fujii, Koutsoliotas, Lemurell, Rubinstein and Yoshida [2] is improved from 45.3236 to 41.54. An application about nonexistence of certain entire L-functions is also provided.