Nonlinear exponential twists of the Liouville function
Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum The main tool we use is Vaughan’s identity for λ(n).
Non-monogenity of multiquadratic number fields
Non-normality of continued fraction partial quotients modulo q
Nonnullity of certain liftings by theta series. (Non nullité de certains relévements par séries théta.)
Non-optimal levels of mod l modular representations.
Non-ordinary primes: A story.
Nonoverlapping Pairs of Explicit Inversive Congruential Pseudorandom Numbers.
Non-possibility to prove infinity of regular primes form some theorems.
Non-primes are recursively divisible.
Nonreciprocal algebraic numbers of small Mahler's measure
We prove that there exist at least cd⁵ monic irreducible nonreciprocal polynomials with integer coefficients of degree at most d whose Mahler measures are smaller than 2, where c is some absolute positive constant. These polynomials are constructed as nonreciprocal divisors of some Newman hexanomials , where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of...
Nonreciprocal algebraic numbers of small measure
The main result of this paper implies that for every positive integer there are at least nonconjugate algebraic numbers which have their Mahler measures lying in the interval . These algebraic numbers are constructed as roots of certain nonreciprocal quadrinomials.
Non-regularity of .
Non-repetitive tilings.
Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties
In this paper we prove some non-solvable base change for Hilbert modular representations, and we use this result to show the meromorphic continuation to the entire complex plane of the zeta functions of some twisted quaternionic Shimura varieties. The zeta functions of the twisted quaternionic Shimura varieties are computed at all places.
Nonsolvable nonic number fields ramified only at one small prime
We prove that there is no primitive nonic number field ramified only at one small prime. So there is no nonic number field ramified only at one small prime and with a nonsolvable Galois group.
Nonstandard arithmetic of iterated polynomials.
Non-trivial solutions to a linear equation in integers
Nontrivial tame extensions over Hopf orders
Non-trivial in the Jacobian of an infinite family of curves of genus 2
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.
Non-Typical Points for β-Shifts
We study sets of non-typical points under the map mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β > 1.541 found in the above paper can be removed.