Results 1 to 10 of about 108,756 (88)

Generalized Pell numbers, balancing numbers and binary quadratic forms [PDF]

Creative Mathematics and Informatics, 2014
In this work, we derive some algebraic identities on generalized Pell numbers and their relationship with balancing numbers. Also we deduce some results on binary quadratic forms involving Pell and balancing numbers.
TEKCAN, AHMET, MERVE, TAYAT
openaire   +2 more sources

On generic and maximal k-ranks of binary forms [PDF]

, 2017
In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number
Lundqvist, Samuel, Oneto, Alessandro, Reznick, Bruce, Shapiro, Boris   +3 more
core   +2 more sources

On cycle integrals of weakly holomorphic modular forms [PDF]

, 2014
In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms.
Bringmann, Kathrin, Guerzhoy, Pavel, Kane, Ben   +2 more
core   +3 more sources

Some new canonical forms for polynomials

, 2013
We give some new canonical representations for forms over $\cc$. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form.
Alexander, Bruce Reznick, Choi, Geramita, Grace, Kung, Kung, Landsberg, Reznick, Richmond, Sylvester, Sylvester, Wakeford   +12 more
core   +2 more sources

Quartic rings associated to binary quartic forms

, 2011
We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava's cubic resolvent rings.
Wood, Melanie Matchett
core   +1 more source

On prime values of binary quadratic forms with a thin variable

, 2018
In this paper we generalize the result of Fouvry and Iwaniec dealing with prime values of the quadratic form $x^2 + y^2$ with one input restricted to a thin subset of the integers.
Lam, Peter Cho-Ho, Schindler, Damaris, Xiao, Stanley Yao   +2 more
core   +1 more source

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

, 2016
Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$.
A Earnest, A Krieg, A Pizer, AG Earnest, H Hijikata, H Hijikata, H Yoshida, HL Resnikoff, J Ellenberg, JS Hsia, M Eichler, M Kneser, M Kneser, P Ponomarev, R Schulze-Pillot, R Schulze-Pillot, R Schulze-Pillot, Rainer Schulze-Pillot, S Böcherer, S Böcherer, S Böcherer, V Blomer, V Blomer, W Duke, W Kohnen   +24 more
core   +1 more source

On the number of cubic orders of bounded discriminant having automorphism group $C_3$, and related problems

, 2013
For a binary quadratic form $Q$, we consider the action of $\mathrm{SO}_Q$ on a two-dimensional vector space. This representation yields perhaps the simplest nontrivial example of a prehomogeneous vector space that is not irreducible, and of a coregular ...
Ariel Shnidman, Davenport, Dedekind, Delone, Hardy, Manjul Bhargava, Sato   +6 more
core   +1 more source

Tabulation of cubic function fields via polynomial binary cubic forms

, 2010
We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound $B$ on the ...
Jacobson Jr., Michael, Rozenhart, Pieter, Scheidler, Renate   +2 more
core   +5 more sources

Nonnegative polynomials and their Carath\'eodory number

, 2014
In 1888 Hilbert showed that every nonnegative homogeneous polynomial with real coefficients of degree $2d$ in $n$ variables is a sum of squares if and only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary quartics).
Naldi, Simone
core   +2 more sources