Swinnerton-Dyer, H. P. F. On l-adic representations and congruences for coefficients of modular forms. (English) Zbl 0267.10032 Modular Functions of one Variable III, Proc. internat. Summer School, Univ. Antwerp 1972, Lect. Notes Math. 350, 1-55 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 74 Documents MSC: 11F03 Modular and automorphic functions 11S31 Class field theory; \(p\)-adic formal groups 14G20 Local ground fields in algebraic geometry PDF BibTeX XML OpenURL Online Encyclopedia of Integer Sequences: Ramanujan’s tau function (or Ramanujan numbers, or tau numbers). Coefficients of unique normalized cusp form Delta_16 of weight 16 for full modular group. Coefficients of unique normalized cusp form Delta_18 of weight 18 for full modular group. Ramanujan tau numbers mod 691 = sum of 11th power of divisors mod 691. Ramanujan function tau(p) as p runs through the primes. a(n) = 1 if n is an odd square, otherwise 0. Weights of cusp forms satisfying certain conditions associated with a theorem of Serre and Deligne. Ramanujan numbers (A000594) read mod 4. Ramanujan numbers (A000594) read mod 8. Ramanujan numbers (A000594) read mod 16. Ramanujan numbers (A000594) read mod 32. Ramanujan numbers (A000594) read mod 64. Ramanujan numbers (A000594) read mod 128. Ramanujan numbers (A000594) read mod 256. Ramanujan numbers (A000594) read mod 512. Ramanujan numbers (A000594) read mod 1024. Ramanujan numbers (A000594) read mod 2048. Ramanujan numbers (A000594) read mod 4096. Ramanujan numbers (A000594) read mod 8192. Ramanujan numbers (A000594) read mod 16384. Ramanujan numbers (A000594) read mod 3. Ramanujan numbers (A000594) read mod 9. Ramanujan numbers (A000594) read mod 27. Ramanujan numbers (A000594) read mod 81. Ramanujan numbers (A000594) read mod 243. Ramanujan numbers (A000594) read mod 729. Ramanujan numbers (A000594) read mod 2187. Ramanujan numbers (A000594) read mod 5. Ramanujan numbers (A000594) read mod 25. Ramanujan numbers (A000594) read mod 125. Ramanujan numbers (A000594) read mod 625. Ramanujan numbers (A000594) read mod 7. Ramanujan numbers (A000594) read mod 7^2. Ramanujan numbers (A000594) read mod 7^3. Ramanujan numbers (A000594) read mod 11. Ramanujan numbers (A000594) read mod 11^2. Ramanujan numbers (A000594) read mod 11^3. Ramanujan numbers (A000594) read mod 13. Ramanujan numbers (A000594) read mod 13^2. Ramanujan numbers (A000594) read mod 13^3. Ramanujan numbers (A000594) read mod 23. Ramanujan numbers (A000594) read mod 23^2. Ramanujan numbers (A000594) read mod 23^3. Exceptional primes for Ramanujan’s tau function.