Let E be an elliptic curve over Q attached to a newform f of weight 2 on 00(N ), and let K be a real quadratic field in which all the primes dividing N are split. This paper relates the canonical R/Z-valued “circle pairing” on E(K ) defined by Mazur and Tate [MT1] to a period integral I ( f, K ) defined in terms of f and K . The resulting conjecture can be viewed as an analogue of the classical...

The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values” of L-functions in terms of cohomological data. The main conjecture of Iwasawa theory describes a p-adic L-function in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for L-functions attached to Dirichlet characters. We use the...

We discuss the problem of finding a p-adic L-function attached to an elliptic curve with complex multiplication over an imaginary quadratic field K, for the case of a prime where the curve has supersingular reduction. While the case of primes of ordinary reduction has been extensively studied and is essentially understood, yielding many deep and interesting results, basic questions remain unans...

Greek-French bilinguals were tested in three masked priming experiments with Greek primes and French targets. Related primes were the translation equivalents of target words, morphologically related to targets, or phonologically related to targets. In Experiment 1, cognate translation equivalents (phonologically similar translations) showed facilitatory priming, relative to matched phonological...

Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a super...

A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction. Successively enlarging the set of primes if needed, this method is guaranteed to work if we restrict ourselves to “good” primes. Depending on the particular app...

Recent studies have found that masked word primes that are orthographic neighbors of the target inhibit lexical decision latencies (Davis & Lupker, 2006; Nakayama, Sears, & Lupker, 2008), consistent with the predictions of lexical competition models of visual word identification (e.g., Grainger & Jacobs, 1996). In contrast, using the fast priming paradigm (Sereno & Rayner, 1992), orthographical...