Showing papers in "Journal of Number Theory in 2019"

TL;DR: In this article, the authors proved the holomorphic modularity of the genus-one four-graviton amplitude in terms of modular functions with one and two loops, respectively.

TL;DR: In this article, the Fourier expansion, Hecke eigenvalues, Atkin-Lehner pseudo-eigenvalues and other data associated to these Eisenstein series, with arbitrary integer weight, level, and nebentypus, were derived in explicit form.

TL;DR: In this paper, the sum ∆ n ⩽ x φ ( ⌊ x / n ⌋ ) involving the Euler functions φ and the integer parts φ of the reciprocals of integers was studied.

TL;DR: In this article, the authors introduced a new summation formula for central values of GL ( 4 ) × GL ( 2 ) L-functions, when varied over Maas forms.

TL;DR: In this paper, the exact value of the η-constant and the multi-wise Davenport constants for finite abelian groups of rank three having the form G ≃ C 2 ⊕ C n 2⊕ c n 3 with 2 | n 2| n 3.

TL;DR: In this article, it was shown that there are infinitely many rational Diophantine sextuples such that the denominators of all the elements in the sextuple are perfect squares.

TL;DR: In this article, it was shown that a D ( 4 ) -quintuple does not exist using both classical and new methods, and a new version of the Rickert's theorem that can be applied on some D 4 -quadruples.

TL;DR: In this paper, it was shown that for 1 c 6 / 5, the Diophantine inequality is solvable in prime numbers p 1, p 2, p 3, p 4, and p 4.

TL;DR: In this paper, the Noether number is defined to be the maximal degree bound for the generators of polynomial invariants of product-one sequences over a multiplicative finite group.

TL;DR: In this article, an explicit version of the Chebotarev theorem for the density of prime ideals with fixed Artin symbol was proved under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.

TL;DR: In this paper, the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions ∑ d 0 − monic & sq. free deg ⁡ d 0 = D L ( 1 2, χ d 0 ) 3 over rational function fields on the order of q 3 4 D.

TL;DR: Garcia et al. as mentioned in this paper considered the case in which A is the image of Z + under a polynomial f ∈ Z [ X ], and gave some conditions under which R ( A ) is dense in Q p.

TL;DR: In this article, the authors studied the Chebotarev-Sato-Tate phenomenon in the case of Hilbert modular forms and derived some unconditional results in the Hilbert modular case.

TL;DR: In this article, the authors generalize the definition of overconvergent p-adic multiple polylogarithms and prove a bound on their norm, and a byproduct of the proof is a characterization of these objects in terms of certain regularized p-adriven iterated integrals.

TL;DR: In this paper, the structure of the idempotent product free sequences of length | S ∖ E (S ) | when the semigroup S is not necessarily finite is determined.

TL;DR: In this article, the theta decomposition of Jacobi forms of nonintegral lattice index is studied for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications.

TL;DR: In this article, the authors derived a criterion for the convergence in distribution as n → ∞ of f ( L n (k ) ) n r k for a wide class of multiplicative arithmetic functions f with polynomial growth r ∈ R.

TL;DR: In this paper, it was shown that the set B 2 of bases in which there exist numbers with exactly two expansions is closed, and that the second smallest element of B 2 is the smallest accumulation point.

TL;DR: In this paper, the authors focus on the Polya group of the compositum of two Galois extensions of Q and show that it is a trivial subgroup of a number field whose polya group is trivial.

TL;DR: In this article, the authors prove polynomial identities which imply Capparelli's partition theorems and derive new Slater type identities involving bases q 2, q 3, q 6, and q 12.

TL;DR: In this article, a natural compactification of the moduli scheme for rank-r Drinfeld F q [T ] -modules with a structure of level N ∈ F q[T ] was studied.

TL;DR: In this article, the authors proved Boyd's conjectures relating Mahler's measures and values of L-functions of elliptic curves in the cases when the corresponding elliptic curve has conductor 14.

TL;DR: In this paper, the authors construct height functions defined stochastically on projective varieties equipped with endomorphisms, and prove that these functions satisfy analogs of the usual properties of canonical heights.

TL;DR: In this article, the authors apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of p k(n) for k ⩾ 1, where n is the number of partitions of an integer n into k-th powers.

TL;DR: In this article, the authors proved a conjecture of Prasad and Takloo-Bighash for discrete series of inner forms of the general linear group over a non-archimedean local field, in the case of Steinberg representations.

TL;DR: In this paper, the authors studied subfields of the Hermitian function field fixed by subgroups that are not contained in the decomposition group of any point except the cyclic subgroups.

TL;DR: In this article, lower bounds for the maximum of the Riemann zeta function S n ( σ, t ) on the interval T β ≤ t ≤ T and near to the critical line, when n ≡ 1 mod 4.

TL;DR: In this article, the authors strengthen the recent result of Cherubini and Guerreiro on the square mean of the error term in the prime geodesic theorem for PSL 2 (Z ).

TL;DR: In this article, Choi and Kim [CK13] gave a canonical basis for the subspace of weakly holomorphic modular forms of weight k on Γ 0 (p ), and investigated its arithmetic properties.