### Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade, IIT Bombay)

### Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade, IIT Bombay)

It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It is meaningful to ask similar questions for systems of several polynomials in several variables of a fixed degree, provided the base field F is finite. […]