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Pairs of cubic forms in many variables

Rainer Dietmann, Trevor D. Wooley (2003)

Acta Arithmetica

Pairs of Quadratic Forms.

William C. Waterhouse (1976)

Inventiones mathematicae

Parameter spaces for quadrics

Anders Thorup (1996)

Banach Center Publications

The parameter spaces for quadrics are reviewed. In addition, an explicit formula for the number of quadrics tangent to given linear subspaces is presented.

Partially defined cocycles and the Maslov index for a local ring

Amedeo Mazzoleni (2004)

Annales de l’institut Fourier

In this paper we study some aspects of the cohomology of groups and we construct a central extension of the symplectic group $S p_{n} (A)$ .

Partitions quadratiques et cyclotomie

Philippe Barkan (1974/1975)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Perfect unary forms over real quadratic fields

Dan Yasaki (2013)

Journal de Théorie des Nombres de Bordeaux

Let $F = ℚ (\sqrt{d})$ be a real quadratic field with ring of integers $𝒪$ . In this paper we analyze the number $h_{d}$ of ${GL}_{1} (𝒪)$ -orbits of homothety classes of perfect unary forms over $F$ as a function of $d$ . We compute $h_{d}$ exactly for square-free $d \leq 200000$ . By relating perfect forms to continued fractions, we give bounds on $h_{d}$ and address some questions raised by Watanabe, Yano, and Hayashi.

Petites solutions des congruences

R. C. BAKER (1982/1983)

Seminaire de Théorie des Nombres de Bordeaux

Pfaffians, central simple algebras and similtudes.

R. Sridharan, M.-A. Knus, R. Parimala (1991)

Mathematische Zeitschrift

Pfaffien et discriminant

Jacques Queyrut (1994)

Journal de théorie des nombres de Bordeaux

Pfister Ideals in Witt Rings.

T.Y. Lam, R. Elman, A.R. Wadsworth (1979)

Mathematische Annalen

Pfister's conjecture on quadratic Co-fields.

David B. Leep (1990)

Journal für die reine und angewandte Mathematik

Picard groups of Witt rings.

Robert W. Fitzgerald (1991)

Mathematische Zeitschrift

Poincaré automorphisms for nondegenerate CR quadrics.

Vladimir Ezov, Gerd Schmalz (1994)

Mathematische Annalen

Polynomial modular n-queens solutions

Jordan Bell (2007)

Acta Arithmetica

Positive inverse Einheiten in komplexen kubischen Zahlkörpern

Reiner Güting (1977)

Acta Arithmetica

Positive-definite quadratic bundles over the plane.

M.-A. Knus, R. Parimala, M. Ojanguren (1982)

Commentarii mathematici Helvetici

Predictive criteria for the representation of primes by binary quadratic forms

Joseph B. Muskat, Blair K. Spearman, Kenneth S. Williams (1995)

Acta Arithmetica

Prime factorization of integral Cayley octaves

Hans Peter Rehm (1993)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Prime producing polynomials: Proof of a conjecture by Mollin and Williams

Anitha Srinivasan (1999)

Acta Arithmetica

Primitive lattice points inside an ellipse

Werner Georg Nowak (2005)

Czechoslovak Mathematical Journal

Let $Q (u, v)$ be a positive definite binary quadratic form with arbitrary real coefficients. For large real $x$ , one may ask for the number $B (x)$ of primitive lattice points (integer points $(m, n)$ with $gcd (M, n) = 1$ ) in the ellipse disc $Q (u, v) \leq x$ , in particular, for the remainder term $R (x)$ in the asymptotics for $B (x)$ . While upper bounds for $R (x)$ depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or...

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