We conjecture that local theta correspondence can be normalized by the leading coefficient of a weighted local period integral, and that there exists a duality of local and global inner product formulas. The conjecture is verified for the pair ( SL2, PGL2) and (SL2, SO(2, 2)). As an application, global inner product formulas are obtained for liftings in the directions PGL2 → SL2, GSO(2, 2) → GL2.

[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...

We present the most comprehensive genetic characterization to date of five Fijian island populations: Viti Levu, Vanua Levu, Kadavu, the Lau Islands, and Rotuma, including nonrecombinant Y (NRY) chromosome and mitochondrial DNA (mtDNA) haplotypes and haplogroups. As a whole, Fijians are genetically intermediate between Melanesians and Polynesians, but the individual Fijian island populations ex...

Joe J. Khalife is a Ph.D. student at the University of California, Riverside and a member of the ASPIN Laboratory. He received a B.E. in Electrical Engineering and an M.S. in Computer Engineering from the Lebanese American University (LAU). From 2012 to 2015, he was a research assistant at LAU. His research interests include opportunistic navigation, autonomous vehicles, and software-defined ra...

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, inc...

Background: Typhoid fever is disease caused by the bacterium Salmonella typhi genus Salmonella. Until now, typhoid still problem health in tropical countries including Indonesia. Knowing risk factor incident at Lau Public Health Center, district, Maros regency 2021
 Method: Research type analytic observational with case control design. The data analysis technique uses chi-square statistica...