The analogue of is then the coordinate ring of (for instance, in the case of the elliptic curve (20) it would be ), with polynomials in this ring producing a set of roots in the curve that is again invariant with respect to the Frobenius action (acting on the and coordinates separately...
Mathematics Asymptotics of families of polynomials and sums of Hurwitz class numbers CLEMSON UNIVERSITY Neil J. Calkin FlowersTimothy BIn a note in the American Mathematical Monthly in 1960, Strodt mentions a way to prove both the Euler-Maclaurin summation formula and the Boole summation formula ...
such as the technique ofquasiminimal excellence(see for example [4]) are expected to yield a good structure theory of definable sets also in higher dimension: a proof of the Quasiminimality Conjecture would likely give thatexponential-algebraic varieties, definable in powers ofusing polynomials and ...
(2013). Roots of random polynomials whose coefficients have logarithmic tails. Ann. Probab. 41, 3542–3581. Google Scholar Kabluchko, Z. and Zaporozhets, D. (2014). Asymptotic distribution of complex zeros of random analytic functions. Ann. Probab. 42, 1374–1395. Google Scholar Kadane,...
We believe that these ideas and concrete results on such a very powerful and versatile tool as exponential sums can find applications to other problems. In particular, in Section 1.4 below we give one of such applications and show that the set of polynomials which are poorly distributed modulo ...
It is horribly slow, as implements a naive algorithm working direclty on bit polynomials. This class is exposed as BitPolynom.The current algorithm is super-linear and takes about 4 seconds to calculate the crc32-sum of 'A'*40000.
Péter Varjú Irreducibility of random polynomials (NTWS 112) 01:00:43 Pierre Le Boudec 2-torsion in class groups of number fields (NTWS 169) 48:10 Ping Xi Analytic approaches towards Katz’s problems on Kloosterman sums (NTWS 13 51:06 Ram Murty Probability Theory and the Riemann Hyp...
The main idea by Kaufman–Lovett uses the Deligne Theorem on multivariate polynomials. The improvement by Rojas-Leon and Wan shows that, for number of points on the curve yp−y=f(x) over Fpn with f(x)∈Fp[x], an extra p can be removed if p is very large compared with polynomial ...
In this section, we collect basic notions and statements on sums of nonnegative circuit polynomials (SONC). Throughout the paper, we use bold letters for vectors, e.g.,x=(x1,…,xn)∈Rn. LetN∗=N∖{0}andR⩾0(R>0) be the set of nonnegative (positive) real numbers. Furthermore...
K.I. Babenko, Approximation by trigonometric polynomials in a certain class of periodic functions of several variables. Dokl. Akad. Nauk SSSR 132, 982–985 (1960) (Russian). English transl. in Soviet Math. Dokl. 1, 672–675 (1960) Google Scholar K.I. Babenko, On the mean convergence...