MEAN VALUES OF CUBIC AND QUARTIC DIRICHLET CHARACTERS

期刊： FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2020; 63 (2)

We evaluate the average of cubic and quartic Dirichlet character sums with the modulus going up to a size comparable to the length of the individual s......

INTEGRAL TRIANGLES AND PERPENDICULAR QUADRILATERAL PAIRS WITH A COMMON AREA AND A COMMON PERIMETER

期刊： FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2020; 63 (2)

By the theory of elliptic curves, we show that there are infinitely many integral right triangle-perpendicular quadrilateral, integral isosceles trian......

ON CERTAIN INTEGRALS INVOLVING THE DIRICHLET DIVISOR PROBLEM

期刊： FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2020; 62 (2)

We prove that integral(X)(1) Delta(x)Delta(3)(x) dx << X-13/9 log(10/3) X, integral(X)(1) Delta(x)Delta(4)(x) dx <<(epsilon) X25/16+epsilo......

ON THE DIOPHANTINE EQUATIONS z(2) = f(x)(2) +/- f(y)(2) INVOLVING LAURENT POLYNOMIALS

期刊： FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2020; 62 (2)

Using the theory of elliptic curves, we study the nontrivial rational (parametric) solutions of the Diophantine equations z(2) = f(x)(2) +/- f(y)(2) f......

A NEW FORMULA FOR MAHLER'S MEASURE

期刊： FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2020; 62 (2)

Let f is an element of Z[x(1), ... , x(N)] be a nonzero polynomial. We show that there exists a sequence of real numbers defined in terms of the coeff......