scholarly journals The circle method and pairs of quadratic forms

2010 ◽  
Vol 22 (2) ◽  
pp. 403-419 ◽  
Author(s):  
Henryk Iwaniec ◽  
Ritabrata Munshi
Keyword(s):  
Quadratic Forms ◽  
Circle Method

scholarly journals Modular forms of degree n and representation by quadratic forms

1979 ◽  
Vol 74 ◽  
pp. 95-122 ◽  
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Circle Method ◽  
Positive Definite ◽  
Siegel Modular Forms ◽  
Partial Result ◽  
Definite Integral ◽  
Integral Matrices

Let A(m), B(n) be positive definite integral matrices and suppose that B is represented by A over each p-adic integers ring Zp. Using the circle method or theory of modular forms in case of n = 1, B, if sufficiently large, is represented by A provided that m ≥ 5. The approach via the theory of modular forms has been extended by [7] to Siegel modular forms to obtain a partial result in the particular case when n = 2, m ≥ 7.

scholarly journals On pairs of quadratic forms in five variables

2021 ◽  
pp. 1-16
Author(s):  
Kummari Mallesham
Keyword(s):  
Upper Bound ◽  
Quadratic Forms ◽  
Circle Method ◽  
Integral Solutions

In this paper, we obtain an upper bound for the number of integral solutions, of given height, of system of two quadratic forms in five variables. Our bound is an improvement over the bound given in [H. Iwaniec and R. Munshi, The circle method and pairs of quadratic forms, J. Théor. Nr. Bordx. 22 (2010) 403–419].

scholarly journals Simultaneous integer values of pairs of quadratic forms

2017 ◽  
Vol 2017 (727) ◽  
Author(s):  
D. R. Heath-Brown ◽  
L. B. Pierce
Keyword(s):  
Quadratic Forms ◽  
Circle Method ◽  
Two Dimensional ◽  
Local Conditions ◽  
Dimensional Version ◽  
Almost All

AbstractWe prove that a pair of integral quadratic forms in five or more variables will simultaneously represent “almost all” pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement.

The circle method with weights for the representation of integers by quadratic forms

2010 ◽  
Vol 171 (6) ◽  
pp. 753-764
Author(s):  
N. Niedermowwe
Keyword(s):  
Quadratic Forms ◽  
Circle Method ◽  
Representation Of Integers

scholarly journals Pairs of diagonal quadratic forms and linear correlations among sums of two squares

2015 ◽  
Vol 27 (4) ◽  
Author(s):  
Timothy D. Browning ◽  
Ritabrata Munshi
Keyword(s):  
Quadratic Forms ◽  
Circle Method ◽  
Sums Of Two Squares ◽  
Integer Solutions ◽  
Linear Correlations

AbstractFor suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares.

Note on quadratic forms over the rational field

1959 ◽  
Vol 55 (3) ◽  
pp. 267-270 ◽  
Author(s):  
J. W. S. Cassels
Keyword(s):  
Quadratic Forms ◽  
Circle Method ◽  
Arithmetic Progressions ◽  
Rational Field ◽  
Dirichlet’S Theorem ◽  
Primes In Arithmetic Progressions ◽  
Dirichlet's Theorem

There is perhaps some methodological interest in developing the theory of quadratic forms over the rational field using only the methods of elementary arithmetic. Hitherto it has appeared necessary to use theorems of a fairly deep nature, most often Dirichlet's theorem about the existence of primes in arithmetic progressions (e.g. Minkowski(1), Hasse(2), Dickson(8), Skolem(9), Burton Jones(6)). Skolem(5) uses a weaker form of Dirichlet's theorem which is rather easier to prove and Siegel(4) uses instead the machinery of the Hardy-Littlewood circle method. In this note I indicate how it is possible to develop the theory of quadratic forms over the rationals without using extraneous resources. Pall(10) states that he has also found such a development of the theory but he does not appear to have published it.

Ultrastructural autoradiography of L6 skeletal-muscle cells exposed to a tritiated macrolide antibiotic (LY237216) in vitro

1992 ◽  
Vol 50 (1) ◽  
pp. 612-613
Author(s):  
S.L. White ◽  
C.B. Jensen ◽  
D.D. Giera ◽  
D.A. Laska ◽  
M.N. Novilla ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
Quantitative Analysis ◽  
Macrolide Antibiotic ◽  
Circle Method ◽  
Apical Surface ◽  
Polycarbonate Membrane ◽  
L6 Cells ◽  
Low Viscosity ◽  
Erythromycin A

In vitro exposure to LY237216 (9-Deoxo-11-deoxy-9,11-{imino[2-(2-methoxyethoxy)ethylidene]-oxy}-(9S)-erythromycin), a macrolide antibiotic, was found to induce cytoplasmic vacuolation in L6 skeletal muscle myoblast cultures (White, S.L., unpubl). The present study was done to determine, by autoradiographic quantitative analysis, the subcellular distribution of 3H-LY237216 in L6 cells.L6 cells (ATCC, CRL 1458) were cultured to confluency on polycarbonate membrane filters (Millipore Corp., Bedford, MA) in M-199 medium (GIBCO® Labs) with 10% fetal bovine serum. The cells were exposed from the apical surface for 1-hour to unlabelled-compound (0 μCi/ml) or 50 (μCi/ml of 3H-LY237216 at a compound concentration of 0.25 mg/ml. Following a rapid rinse in compound-free growth medium, the cells were slam-frozen against a liquid nitrogen cooled, polished copper block in a CF-100 cryofixation unit (LifeCell Corp., The Woodlands, TX). Specimens were dried in the MDD-C Molecular Distillation Drier (LifeCell Corp.), vapor osmicated and embedded in Spurrs low viscosity resin. Ultrathin sections collected on formvar coated stainless steel grids were counter-stained, then individually mounted on corks. A monolayer of Ilford L4 nuclear emulsion (Polysciences, Inc., Warrington, PA) was placed on the sections, utilizing a modified “loop method”. The emulsions were exposed for 7-weeks in a light-tight box at 4°C. Autoradiographs were developed in Microdol-X developer and examined on a Philips EM410LS transmission electron microscope. Quantitative analysis of compound localization employed the point and circle approach of Williams; incorporating the probability circle method of Salpeter and McHenry.

Sign in / Sign up

Export Citation Format

Share Document