A368381 Integers k for which there is a lacunary modular form of weight k/2 which is a product of eta functions.

1, 2, 3, 4, 6, 8, 10, 14, 18, 26

Offset

1,2

Comments

Borcherds remarks that this is also the list of numbers k such that there are modular forms on the orthogonal group O_{k,2}(R) which can be written as an "interesting infinite product".

References

R. E. Borcherds, (1994). Sporadic groups and string theory. In First European Congress of Mathematics: Paris, July 6-10, 1992 Volume I Invited Lectures (Part 1) (pp. 411-421). Basel: Birkhäuser Basel. [This is different from the article in the link below. Do not delete this reference.]

Links

Table of n, a(n) for n=1..10.

R. E. Borcherds, Sporadic groups and string theory (Expanded version of talk referenced above).

F. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652.

J.-P. Serre, Sur la lacunarité des puissances de eta, Glasgow Mathematical Journal 27 (1985) 203-221. [Borcherds remarks that this reference omits the number 18, however the form eta(q)^9*eta(q^2)^9 of weight 18/2 appears to be lacunary.]

Crossrefs

Sequence in context: A274194 A237751 A045476 * A323360 A375186 A297417

Adjacent sequences: A368378 A368379 A368380 * A368382 A368383 A368384

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Feb 26 2024

Status

approved