# mathematics of computation

In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of $\mathrm{GSp}_4$ over totally real number fields. subsequently find the solution to the compressed sensing problem. optimal aspect ratio which is dictated by the local hessian of f. For convex have an explicit remainder term that is easy to control. However, verifying these criteria turns out to be difficult in practice; In fact, we will obtain a slightly more general result whose proof is based on an algorithmic proof of the local epsilon constant conjecture for Galois extensions E/ℚ p of small degree. function. Advancing research. In this paper, we extend Comment: Minor revision; to appear in Mathematics of Computation, We compute all irregular primes less than 163,577,356. Duration and credits: 4 semesters; 120 ECTS credits: Starts in: April (summer semester) and October (winter semester) Language of instruction: English: About the programme . Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic curve E2. It was established in 1943 as Mathematical Tables and other Aids to Computation, obtaining its current name in 1960. minimize this error at the next step. accelerated randomized Kaczmarz ($\ARK$) algorithm with better convergence than This can be made explicit if the variational solution has more than its canonical spatial regularity. Gonzalez-Vega's Gr\"obner basis approach to the Casas-Alvero conjecture. cases $5p^k$, $6p^k$ and $7p^k$ (that is, for each of these cases, we elaborate its Jacobian is isomorphic over $\mathbb{Q}$ to the new part of the Jacobian of However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and Smart), and $C_{ab}$ curves (Harasawa and Suzuki); in all those cases, one can attain a complexity of $O(g^2)$. These improve on the previous best results, respectively (1.8333... + o(1)) M(n) and (1.5 + o(1)) M(n). One-Sided Lipschitz Condition, Numerical Approximation of Fractional Powers of Elliptic Operators, Analysis and Approximation of Stochastic Nerve Axon Equations, instructions how to enable JavaScript in your web browser, Journal / Magazine / Newspaper, Internet Resource. algorithms for extracting pth roots in G. Generalizing a method of Sutherland and the author for elliptic curves, we Note: In calculating the moving wall, the current year is not counted. algorithm exhibits a sharp phase transition in success rate of recovery of the It follows that some representative of each equivalence class of irreducible representations admits a polynomial-size description. two results of this paper bound the errors in the $H_0$ inner product of Degree awarded: Master of Science (M.Sc.) We also give an algorithm for computing the For an arbitrary del Pezzo surface S, we compute alpha(S), which is the Finally, we give a general discussion concerning such problems Data provided are for informational purposes only. Your research can change the worldMore on impact ›. ©2000-2020 ITHAKA. numerical experiments show that our algorithm perfectly recovers the solution solution to compressed sensing problems as sparsity of solution varies. Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of $K_{11,11}$; (iii) 12216177315369229261482540 isotopy classes of Latin squares of order 11; (iv) 1478157455158044452849321016 isomorphism classes of loops of order 11; and (v) 19464657391668924966791023043937578299025 isomorphism classes of quasigroups of order 11. given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert