The ring of differential Fourier expansions

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• 作者：Alexandru Buium ; ^{buium@math.unm.edu} ; Arnab Saha ^{arnab@math.unm.edu}
• 关键词：11F32 ; 11F85
• 刊名：Journal of Number Theory
• 出版年：2012
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：May, 2012
• 卷：132
• 期：5
• 页码：896-937
• 文件大小：428 K

摘要

For a fixed prime we prove structure theorems for the kernel and the image of the map that attaches to any differential modular function its differential Fourier expansion. The image of this map, which is the ring of differential Fourier expansions, plays the role of ring of functions on a 鈥渄ifferential Igusa curve鈥? Our constructions are then used to perform an analytic continuation between isogeny covariant differential modular forms on the differential Igusa curves belonging to different primes.