Congruences between modular forms given by the dividedβfamily in homotopy theory
Mark Joseph Behrens · Geometry & Topology · 2009
We characterize the 2-line of the p -local Adams-Novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p 5. We give a similar characterization of the 1-line, reinterpreting some earlier work of A Baker and G Laures.These results are then used to deduce that, for `a prime which generates Z p , the spectrum Q.`/ detects the ˛and ˇfamilies in the stable stems.