Supercongruences satisfied by coefficients of 2F1 hypergeometric series

Recently, Chan, Cooper and Sica conjectured two congruences for coefficients of classical 2F1 hypergeometric series which also arise from power series expansions of modular forms in terms of modular functions. We prove these two congruences using combinatorial properties of the coefficients.Comment: 13 page

Multiplicative functions arising from the study of mutually unbiased bases

We embed the somewhat unusual multiplicative function, which was serendipitously discovered in 2010 during a study of mutually unbiased bases in the Hilbert space of quantum physics, into two families of multiplicative functions that we construct as generalizations of that particular example. In addition, we report yet another multiplicative function, which is also suggested by that example; it can be used to express the squarefree part of an integer in terms of an exponential sum.Comment: 16 pages; v4 largely identical with v3 except for a few minor edit

Loss of viability during freeze-thaw of intact and adherent human embryonic stem cells with conventional slow-cooling protocols is predominantly due to apoptosis rather than cellular necrosis

10.1007/s11373-005-9051-9Journal of Biomedical Science133433-44

Enteropathy-associated T cell lymphoma subtypes are characterized by loss of function of SETD2

Enteropathy-associated T cell lymphoma (EATL) is a lethal, and the most common, neoplastic complication of celiac disease. Here, we defined the genetic landscape of EATL through whole-exome sequencing of 69 EATL tumors. SETD2 was the most frequently silenced gene in EATL (32% of cases). The JAK-STAT pathway was the most frequently mutated pathway, with frequent mutations in STAT5B as well as JAK1 , JAK3 , STAT3 , and SOCS1 . We also identified mutations in KRAS , TP53 , and TERT . Type I EATL and type II EATL (monomorphic epitheliotropic intestinal T cell lymphoma) had highly overlapping genetic alterations indicating shared mechanisms underlying their pathogenesis. We modeled the effects of SETD2 loss in vivo by developing a T cell–specific knockout mouse. These mice manifested an expansion of γδ T cells, indicating novel roles for SETD2 in T cell development and lymphomagenesis. Our data render the most comprehensive genetic portrait yet of this uncommon but lethal disease and may inform future classification schemes

On the Ramanujan-Gollinitz-Gordon Continued Fraction

[[abstract]]We derive many new identities involving the Ramanujan-Göllnitz-Gordon continued fraction H(q). These include relations between H(q) and H(q n ) , which are established using modular equations of degree n. We also evaluate explicitly H(q) at q = e - pÖn /2q=e−n2 for various positive integers n. Using results of M. Deuring, we show that H( ±e - pÖn /2 )H(e−n2) are units for all positive integers n