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A346293
Maximum possible order of the automorphism group of a compact Riemann surface of genus n.
7
48, 168, 120, 192, 150, 504, 336, 320, 432, 240, 120, 360, 1092, 504, 720, 1344, 168, 720, 228, 480, 1008, 192, 216, 720, 750, 624, 1296, 672, 264, 720, 372, 1536, 1320, 544, 672, 1728, 444, 912, 936, 960, 410, 1512, 516, 1320, 2160, 384, 408
OFFSET
2,1
COMMENTS
By Hurwitz's automorphisms theorem, a(n) <= 84*(n-1). The values n such that a(n) = 84*(n-1) are listed in A179982.
Breuer's book erroneously gives a(33) = 768. (See errata.) - Eric M. Schmidt, Jul 29 2021
REFERENCES
Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000.
EXAMPLE
The Bolza surface is a compact Riemann surface of genus 2 whose automorphism group is of the highest possible order (order 48, isomorphic to GL(2,3)), so a(2) = 48.
CROSSREFS
Cf. A179982.
Sequence in context: A044761 A248456 A370126 * A244178 A131683 A066134
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Jul 13 2021
EXTENSIONS
a(12)-a(48) from Eric M. Schmidt, Jul 29 2021
STATUS
approved