The mock theta functions, possibly the most famous and the deepest topic in Ramanujan's lost notebook, were first introduced by Ramanujan in his last letter to G. H. Hardy. In his letter, he called a function f(q) defined by a power series in q which converges for |q|<1 a mock theta function if it satisfies. (1) For every root of unity c, there is… (More)
We show the existence of the Chow–Künneth projectors for certain varieties, including Kuga–Shimura varieties of Hilbert modular varieties. The Chow–Künneth projectors of a smooth projective variety are, by definition, mutually orthogonal idempotents of the Chow ring of self-correspondences which give decomposition of the total cohomology of the variety into… (More)
Let k = p 1 a 1 p a 2 2 · · · p am m be the prime factorization of a positive integer k and let b k (n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k.
The main result of this paper is the proof for elliptic modular threefolds of some conjectures formulated by the second-named author and shown by Jannsen to be equivalent to a conjecture of Beilinson on the filtration on the Chow groups of smooth projective varieties. These conjectures are known to be true for surfaces in general, but for elliptic modular… (More)
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In the spirit of the conference theme, <i>the interplay between autonomy and intelligence</i>, the general direction of this paper is to describe how autonomous robots could begin to autonomously develop intelligence. (For us a robot is always a constructed, embodied, situated system.) Most of the discussion will take place at the abstract level of system… (More)