scholarly journals Weyl's inequality and exponential sums over binary forms

2000 ◽  
Vol 28 (0) ◽  
pp. 83-95 ◽  
Author(s):  
Trevor D. Wooley
Bach ◽  
2018 ◽  
Vol 49 (2) ◽  
pp. 281
Author(s):  
Brody
Keyword(s):  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hassan Hakimi ◽  
Masahito Asada ◽  
Takahiro Ishizaki ◽  
Shinichiro Kawazu

AbstractBabesia parasite invades exclusively red blood cell (RBC) in mammalian host and induces alterations to host cell for survival. Despite the importance of Babesia in livestock industry and emerging cases in humans, their basic biology is hampered by lack of suitable biological tools. In this study, we aimed to develop a synchronization method for Babesia bovis which causes the most pathogenic form of bovine babesiosis. Initially, we used compound 2 (C2), a specific inhibitor of cyclic GMP-dependent protein kinase (PKG), and a derivative of C2, ML10. While both inhibitors were able to prevent B. bovis egress from RBC and increased percentage of binary forms, removal of inhibitors from culture did not result in a synchronized egress of parasites. Because using PKG inhibitors alone was not efficient to induce a synchronized culture, we isolated viable and invasive B. bovis merozoites and showed dynamics of merozoite invasion and development in RBCs. Using isolated merozoites we showed that BbVEAP, VESA1-export associated protein, is essential for parasite development in the RBC while has no significant role in invasion. Given the importance of invasion for the establishment of infection, this study paves the way for finding novel antigens to be used in control strategies against bovine babesiosis.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.


2001 ◽  
Vol 163 ◽  
pp. 13-53 ◽  
Author(s):  
Jörg Brüdern ◽  
Trevor D. Wooley

We establish that almost all natural numbers not congruent to 5 modulo 9 are the sum of three cubes and a sixth power of natural numbers, and show, moreover, that the number of such representations is almost always of the expected order of magnitude. As a corollary, the number of representations of a large integer as the sum of six cubes and two sixth powers has the expected order of magnitude. Our results depend on a certain seventh moment of cubic Weyl sums restricted to minor arcs, the latest developments in the theory of exponential sums over smooth numbers, and recent technology for controlling the major arcs in the Hardy-Littlewood method, together with the use of a novel quasi-smooth set of integers.


2014 ◽  
Vol 13 (06) ◽  
pp. 1450013 ◽  
Author(s):  
Francis N. Castro ◽  
Ivelisse M. Rubio

We present an elementary method to compute the exact p-divisibility of exponential sums of systems of polynomial equations over the prime field. Our results extend results by Carlitz and provide concrete and simple conditions to construct families of polynomial equations that are solvable over the prime field.


1967 ◽  
Vol 6 (2) ◽  
pp. 157-184 ◽  
Author(s):  
Warren May
Keyword(s):  

Author(s):  
PALOMA BENGOECHEA

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.


Sign in / Sign up

Export Citation Format

Share Document