TY - JOUR

T1 - Forms of higher degree over certain fields

AU - Glazman, A.L.

AU - Zatitski, P.B.

AU - Sivatski, A.S.

AU - Stolyarov, D.M.

PY - 2013

Y1 - 2013

N2 - Let F be a nonformally real field, n, r be positive integers. Suppose that for any prime number p ≤ n, the quotient group F*/F*p is finite. We prove that if N is large enough, then any system of r forms of degree in N variables over F has a nonzero solution. Also we show that if, in addition, F is infinite, then any diagonal form with nonzero coefficients of degree n in {pipe}F*/F*n{pipe} variables is universal, i.e., its set of nonzero values coincides with F* Bibliography: 4 titles. © 2013 Springer Science+Business Media New York.

AB - Let F be a nonformally real field, n, r be positive integers. Suppose that for any prime number p ≤ n, the quotient group F*/F*p is finite. We prove that if N is large enough, then any system of r forms of degree in N variables over F has a nonzero solution. Also we show that if, in addition, F is infinite, then any diagonal form with nonzero coefficients of degree n in {pipe}F*/F*n{pipe} variables is universal, i.e., its set of nonzero values coincides with F* Bibliography: 4 titles. © 2013 Springer Science+Business Media New York.

U2 - 10.1007/s10958-013-1150-y

DO - 10.1007/s10958-013-1150-y

M3 - Article

SP - 591

EP - 595

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -