research topics in number theory

The distribution of non-Parry Perron numbers and their conjugates

Completing an universal m -gonal form with a closing unary piece

The paramodular Hecke algebra

Integral points on a del Pezzo surface over imaginary quadratic fields

Chow groups of one-dimensional noetherian domains

Rankin–Cohen type differential operators on Hermitian modular forms

Weighted and restricted sum formulas of Euler sums

The shifted convolution L-function for Maass forms

Linear system of hypersurfaces passing through a Galois orbit

Asymptotics of commuting \(\ell \) -tuples in symmetric groups and log-concavity

\(\ell \) -Adic properties and congruences of \(\ell \) -regular partition functions

Vanishing coefficients in two q -series related to Legendre-signed partitions

Correction: Quadratic points on dynamical modular curves

Transcendental nature of p -adic digamma values

On log-concavity of the number of orbits in commuting tuples of permutations

A spectral theorem for compact representations and non-unitary cusp forms

Bounding the order of vanishing of cuspidal newforms via the n th centered moments

Asymptotic expansion for the Fourier coefficients associated with the inverse of the modular discriminant function \(\Delta \)

On fake subfields of number fields

Sum representations of Appell–Lauricella functions over finite fields using confluent hypergeometric functions and their applications

Large sieve inequalities for periods of Maass forms

Congruences for Siegel modular forms of nonquadratic nebentypus mod p

On the conjecture of Erdős, Joò and Komornik for p -adic numbers

Transcendence of certain sequences of algebraic numbers.

Higher Turán inequalities for the plane partition function

Publisher Correction: Field change for the Cassels–Tate pairing and applications to class groups

Rank deviations for overpartitions

Curious subgroups of \({\text {GL}}(2, {\mathbb {Z}}/ N {\mathbb {Z}})\) as direct products of groups of distinct prime-power level

A new bound for the orthogonality defect of HKZ reduced lattices

Minimal resolutions of Iwasawa modules

Elliptic normal curves of even degree and theta functions

Distribution of angles to lattice points seen from a fast moving observer

Field change for the Cassels–Tate pairing and applications to class groups

Right-angled triangles with almost prime hypotenuse

Quadratic points on dynamical modular curves

Misiurewicz polynomials and dynamical units, part II

Primitive algebraic points on curves

The T -adic Galois representation is surjective for a positive density of Drinfeld modules

Periodicity and pure periodicity in alternate base systems.

Ratios conjecture for quadratic twists of modular L -functions

Lambda-invariants of Mazur–Tate elements attached to Ramanujan’s tau function and congruences with Eisenstein series

On the local constancy of certain mod p Galois representations

On Pillai’s Problem involving Lucas sequences of the second kind

Macmahon’s sums-of-divisors and their connection to multiple Eisenstein series

On the quasi-periodic Schneider continued fractions

Torsion primes for elliptic curves over degree 8 number fields

Equidistribution of solutions of ternary quadratic congruences modulo prime powers.

The Turán and Laguerre inequalities for quasi-polynomial-like functions

A bijection for tuples of commuting permutations and a log-concavity conjecture

Diophantine triples with three parameters