scholarly journals A new form of the circle method, and its application to quadratic forms.

1996 ◽  
Vol 1996 (481) ◽  
pp. 149-206 ◽  
Keyword(s):  
Quadratic Forms ◽  
Circle Method ◽  
New Form

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 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.

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 Classifying Quadratic Forms Over Z2 in Five Variables

2019 ◽  
pp. 1-6
Author(s):  
Amrita Acharyya ◽  
Gerard Thompson
Keyword(s):  
Quadratic Forms ◽  
New Form

Quadratic forms in ve variables over the eld Z2 are classified by extending results previously obtained for four variables. It is shown that only one new form genuinely involving ve variables appears.

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.

Fine Structure of Platelet Interaction with a New Microcrystalline Collagen Preparation

1974 ◽  
Vol 32 ◽  
pp. 58-59
Author(s):  
W. H. Zucker ◽  
R. G. Mason
Keyword(s):  
Fine Structure ◽  
Platelet Aggregation ◽  
Hydrochloric Acid ◽  
Whole Blood ◽  
Platelet Adhesion ◽  
Hemostatic Agent ◽  
Native Collagen ◽  
Fibrillar Morphology ◽  
Clinical Interest ◽  
New Form

Platelet adhesion initiates platelet aggregation and is an important component of the hemostatic process. Since the development of a new form of collagen as a topical hemostatic agent is of both basic and clinical interest, an ultrastructural and hematologic study of the interaction of platelets with the microcrystalline collagen preparation was undertaken.In this study, whole blood anticoagulated with EDTA was used in order to inhibit aggregation and permit study of platelet adhesion to collagen as an isolated event. The microcrystalline collagen was prepared from bovine dermal corium; milling was with sharp blades. The preparation consists of partial hydrochloric acid amine collagen salts and retains much of the fibrillar morphology of native collagen.

The staining pattern of the tropomyosin sequence is displayed in a new paracrystal

1986 ◽  
Vol 44 ◽  
pp. 150-151
Author(s):  
M.K. Lamvik ◽  
L.L. Klatt
Keyword(s):  
Amino Acid ◽  
Amino Acid Sequence ◽  
Staining Pattern ◽  
Banding Patterns ◽  
Mass Thickness ◽  
New Form

Tropomyosin paracrystals have been used extensively as test specimens and magnification standards due to their clear periodic banding patterns. The paracrystal type discovered by Ohtsuki1 has been of particular interest as a test of unstained specimens because of alternating bands that differ by 50% in mass thickness. While producing specimens of this type, we came across a new paracrystal form. Since this new form displays aligned tropomyosin molecules without the overlaps that are characteristic of the Ohtsuki-type paracrystal, it presents a staining pattern that corresponds to the amino acid sequence of the molecule.

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