zbMath0253.10002MaRDI QIDQ5666618
Hans Rademacher
Publication date: 1973
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Congruences and asymptotics of Andrews' singular overpartitions,
On the uniform distribution (mod 1) of the Farey fractions and \(\ell ^ p\) spaces,
On a class of elliptic functions associated with even Dirichlet characters,
Note on a theorem of Farkas and Kra,
Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials,
On missing trace values for the eta multipliers,
A formula for the partition function that ``counts, On representations by determinants of p(n) and \(p_ m(n)\), On the denominator of generalized Bernoulli numbers, Spectral square means for period integrals of wave functions on real hyperbolic spaces, On the asymptotic distribution of cranks and ranks of cubic partitions, The size of the Selberg zeta-function at places symmetric with respect to the line \(\mathrm{Re}(s)=1/2\), On a limit problem in Ford circles, Monogénéité de l'anneau des entiers de certains corps de classes de rayon. (Monogeneity of the ring of integers of certain ray class fields), Dedekind sums and uniform distribution, Finite groups and Hecke operators, A note on the equation \(1^ k+2^ k+\cdots+(x-1)^ k=y^ m\), About a theorem of Paolo Codecà's and \(\Omega\)-estimates for arithmetical convolutions, Digit variance and Dedekind sums, Asymptotic formulas for some restricted partition functions, On the GLY conjecture of upper estimate of positive integral points in real right-angled simplices, Limiting distributions for the number of distinct component sizes in relational structures, A unified approach to the integrals of Mellin-Barnes-Hecke type, A direct approach to the Mellin transform, \( \mathcal{N} = 4 \) superconformal algebra and the entropy of hyperkähler manifolds, Parallel version of the universal Vassiliev-Kontsevich invariant, On small zeros of quadratic forms over finite fields, Analysis of some new partition statistics, Asymptotics of McKay numbers for \(S_n\), On the restriction map for Jacobi forms, Degenerate and character Dedekind sums, On a conjecture of B. Berndt and B. Kim, On the order of the error function of the square-full integers, On the Diophantine equation \(1^k+2^k+\dots +x^k+R(x)=y^2\), On the arithmetic of special values of L functions, Nonlinear differential equations satisfied by certain classical modular forms, Apollonian circle packings: Number theory, On generalized Dedekind sums involving quasi-periodic Euler functions, On the transformation equation for the partition generating function, On a conjecture of Chowla and Walum, Applications of the theory of modular forms to number theory, Some non-congruence subgroups and the associated modular curves, On a conjecture of S. Chowla and of S. Chowla and H. Walum. I, Fractional part sums and divisor functions, The asymptotic behaviour of the binomial circulant determinant, On a remarkable formula of Ramanujan, Theta function identities, Special functions related to Dedekind-type DC-sums and their applications, A theta function identity of degree eight and Eisenstein series identities, Asymptotics of an ordinary differential equation and the Riemann hypothesis, Scaled asymptotics for some \(q\)-functions, A note on the denominators of Bernoulli numbers, Zeros of derivatives of Riemann's xi-function on the critical line, Minimal triangulations of sphere bundles over the circle, Quelques remarques sur les familles canoniques de polynômes générateurs pour l'exponentielle. (Remarks about the canonical families of polynomials that generate the exponential.), Power series and zeroes of trinomial equations, On the relation between units and Jacobi sums in prime cyclotomic fields, On the Andrews-Zagier asymptotics for partitions without sequences, A symbolic decision procedure for relations arising among Taylor coefficients of classical Jacobi theta functions, The Rademacher conjecture and \(q\)-partial fractions, On the theta-multiplier system, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Classification of two-person ordinal bimatrix games, Upper bounds on \(L(1,\chi)\) taking into account ramified prime ideals, Sum formulas of multiple zeta values with arguments multiples of a common positive integer, A Rademacher type formula for partitions and overpartitions, On representations of positive integers as a sum of two polynomials, A new approach to \(q\)-Bernoulli numbers and \(q\)-Bernoulli polynomials related to \(q\)-Bernstein polynomials, Dedekind sums and generalizations of the Markov Diophantine equation, From Planck to Ramanujan: a quantum \(1/f\) noise in equilibrium, A unified presentation of identities involving Weierstrass-type functions and their applications, On formal fractions associated with the symmetric groups, Mellin's formula and some combinatorial identities, A reciprocity formula for quadratic forms, Sur les entiers n pour lesquels il y à beaucoup de groupes abéliens d'ordre \(n\), Equidistribution of Heegner points and the partition function, Pseudo-random numbers and optimal coefficients, Codes over GF(4) and complex lattices, Asymptotic behavior of multiplicative functions, Formulas for sums of powers of integers by functional equations, On recurrence relations for the extensions of Euler sums, Supersingular parameters of the Deuring normal form, On the ratio of two blocks of consecutive integers, Asymptotic expansions for the coefficients of analytic generating functions, Simple upper bounds for partition functions, Generalized balancing numbers, Bernoulli numbers and polynomials via residues, Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions, Combinatorial numbers in binary recurrences, On the order of the error function of the square-full integers. II, On the sets represented by the partitions of an integer \(n\), Integral theorem on large deviations of integer-valued additive functions, A matrix partition problem, Une conjecture de Chowla et Walum. (A conjecture of Chowla and Walum), About a theorem of Paolo Codecà's and \(\Omega\)-estimates for arithmetical convolutions: Addendum, Eine Note zur Gleichverteilung additiv erzeugter Folgen. (A note on the uniform distribution of additively generated sequences.), The monster Lie algebra, A quadratic divisor problem, Modular symbols, Eisenstein series, and congruences, Integral and series representations of q-polynomials and functions: Part III theta, Ramanujan and q-Bessel functions, The scattering map determines the nonlinearity, The distribution of certain special values of the cubic Legendre symbol, Estimates for vector-valued holomorphic functions and Littlewood–Paley–Stein theory, Counting nilpotent Galois extensions, An arithmetic formula for the partition function, The Variation of the De Rham Zeta Function, Balancing with binomial coefficients, SUMS OF POWERS WITH Fk NUMBERS, On the Number of Convex Lattice Polygons, The asymptotic expansion of certain series considered by ramanujan, Study of rational cubic forms via the circle method [after D.R. Heath-Brown, C. Hooley, and R.C. Vaughan], Iterated elliptic and hypergeometric integrals for Feynman diagrams, Monodromy and Picard-Fuchs equations for families of $K3$-surfaces and elliptic curves, Rademacher-type formulas for the multiplicities of irreducible highest-weight representations of affine Lie algebras, Le calcul des invariants $\theta_p$ des espaces lenticulaires, The number of partitions with distinct even parts revisited, Unnamed Item, Detailed asymptotic expansions for partitions into powers, On Demailly's \(L^2\) extension theorem from non-reduced subvarieties, Periodic partial theta functions and \(q\)-hypergeometric knot multisums as quantum Jacobi forms, A single-variable proof of the omega SPT congruence family over powers of 5, The arithmetic of modular grids, Hook length biases and general linear partition inequalities, On the infinite Borwein product raised to a positive real power, Loop-by-loop differential equations for dual (elliptic) Feynman integrals, Proofs of two conjectural Andrews–Beck type congruences due to Lin, Peng and Toh, Additive evaluations of the number of divisors, Stability estimates for the recovery of the nonlinearity from scattering data, Higher order Turán inequalities for the distinct partition function, Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters, Further insights into the mysteries of the values of zeta functions at integers, Character analogues of Cohen-type identities and related Voronoï summation formulas, Stationary measure for the open KPZ equation, On Series of Ordinals and Combinatorics, The modular group and a hyperbolic beta integral, A Partition Function Connected with the Göllnitz–Gordon Identities, Faulhaber's Formula, Odd Bernoulli Numbers, and the Method of Partial Sums, Some families of Weierstrass-type functions and their applications, A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials, An improved upper bound for the argument of the Riemann zeta-function on the critical line, ON EVALUATION OF GENERALIZED EULER SUMS OF EVEN WEIGHT, Genus character L‐functions of quadratic orders and class numbers, Quantum Modular Forms and Singular Combinatorial Series with Distinct Roots of Unity, Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas, Quantum modular forms and singular combinatorial series with repeated roots of unity, Upper bounds on $L(1,\chi )$ taking into account a finite set of prime ideals, An analogue of the von Staudt-Clausen theorem, Congruences satisfied by eta-quotients, Symplectic quantum mechanics and Chern-Simons gauge theory. II. Mapping tori of tori, Convolution formulae for Bernoulli numbers, Two complementary relations for the Rogers-Ramanujan continued fraction, Explicit bounds for residues of Dedekind zeta functions, values of \(L\)-functions at \(s=1\), and relative class numbers, A Proof of some identities of Ramanujan using modular forms, On a kind of divisor problem. II, Ein dreidimensionales Gitterpunktproblem, Zeros of the dilogarithm, Triple product identities for the Jacobi symbol, A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity, Unnamed Item, Further evidence for the conformal structure of a Schwarzschild black hole in an algebraic approach, ON THE BROKEN 1-DIAMOND PARTITION, Modular forms of rational weights and modular varieties, Automorphic forms, fake monster algebras, and hyperbolic reflection groups, Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface, On the distribution of Galois groups, \({\mathcal N}=2\) superconformal algebra and the entropy of Calabi-Yau manifolds, Shimura lifting of modular forms of weight \(3/2\), Sum formulas of multiple zeta values with selected arguments, Reflective automorphic forms on lattices of squarefree level, Integral representations for certain series, Improvements to Turing’s method, Mock Theta Functions Ranks and Maass Forms, The graphs of exponential sums, VALEURS IMPAIRES DE LA FONCTION DE PARTITION p(n), Computing the integer partition function, The sequence of fractional parts of roots, Laplace transforms and the Riemann zeta function, A note on Bernoulli identities associated with the Weierstrass ℘-function, Newton polynomials and a class of Diophantine equations, ON THE ASYMPTOTIC EXPANSION OF THE QUANTUM SU(2)<i> </i>INVARIANT AT <i>ζ =</i> <i>e</i><sup>4</sup><i><sup>πi/r </sup></i>FOR LENS SPACE <i>L</I> (<i>p, q</i>), Integral and series representations of 𝑞-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities, An asymptotic formula for a trigonometric sum of Vinogradov, Discrete mean square of the coefficients of symmetric square \(L\)-functions on certain sequence of positive numbers, Quantum modularity of partial theta series with periodic coefficients, On the number of convex lattice polytopes, Partitions and Sylvester waves, Some integral and asymptotic formulas associated with the Hurwitz zeta function, On the number of primitive representations of integers as sums of squares, Elliptic function based algorithms to prove Jacobi theta function relations, On Two Lacunary Series and Modular Curves, Jacobi's four and eight squares theorems and partitions into distinct parts, Faà di Bruno's formula and modular forms, On the Hannay–Ozorio De Almeida Sum Formula, Rees Algebras and Mixed Multiplicities, Overpartition ranks and quantum modular forms, On theta-type functions in the form \((x; q)_\infty\), Limits of Jensen polynomials for partitions and other sequences, On the general asymmetric divisor problem, Effective estimates for the smallest parts function, Cusp forms of weight 1 associated to Fermat curves, On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\), The Korteweg-de Vries equation and a Diophantine problem related to Bernoulli polynomials, Efficiency functionals for the Lévy flight foraging hypothesis, Irreducibility of the zero polynomials of Eisenstein series, Asymptotic formulas for spt-crank of partitions, General modular quantum dilogarithm and beta integrals, A model of solute transport through stratum corneum using solute capture and release, The estimates of trigonometric sums and new bounds on a mean value, a sequence and a cryptographic function, Identities associated to a generalized divisor function and modified Bessel function, An improved upper bound for the argument of the Riemann zeta-function on the critical line. II, Sum formulas of multiple zeta values with even arguments and polynomial weights, On the \(r\)-th root partition function. II., Quantum Jacobi forms and balanced unimodal sequences, A summary of Euler's work on the pentagonal number theorem, Mock modular forms and \(d\)-distinct partitions, Dedekind sums with roots of unity and their reciprocity law, Multiple convolution formulae of Bernoulli and Euler numbers, Easy proofs of Riemann’s functional equation for $\zeta (s)$ and of Lipschitz summation, A note on the restriction map for Jacobi forms, Counting the number of solutions to certain infinite Diophantine equations, Special factors of holomorphic eta quotients, On asymptotics of \(q\)-Gamma functions, Remarks on the generalized Lindelöf hypothesis, Character sums and the series L(1, χ), On the general transformation of the Wirtinger integral, The Hurwitz zeta function as a convergent series, Quasimodular forms and \(s\ell (m|m)^\wedge\) characters, Algorithms for enumeration problem of linear congruence modulo \(m\) as sum of restricted partition numbers, Explicit estimates for the Riemann zeta function, On the maximal multiplicity of parts in a random integer partition, Curve fitting, differential equations and the Riemann hypothesis, Generalized Verma modules, loop space cohomology and MacDonald-type identities, Weight of a link in a shortest path tree and the Dedekind Eta function, An alternative transformation formula for the Dedekind η-function via the Chinese Remainder Theorem, On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions, Finite differences of the logarithm of the partition function, A two-variable generalization of the Kummer-Malmstén formula for the logarithm of the double gamma and double sine functions, Wronskians of theta functions and series for \(1/\pi\), A simple recursion for power sum polynomials, The minimum of the levels of the proper factors of a holomorphic eta quotient, Quantum mock modular forms arising from eta-theta functions, Hyperbolic Fourier coefficients of Poincaré series, Finding modular functions for Ramanujan-type identities, The combinatorics of MacMahon's partial fractions, On the distribution of zeros of derivatives of the Riemann \(\xi \)-function, Disproof of a conjecture by Rademacher on partial fractions, Asymptotics for the partial fractions of the restricted partition generating function I, A Hardy-Ramanujan formula for restricted partitions, Exact asymptotic formulas for the coefficients of nonmodular functions, Some identities for the partition function, Another congruence for the Apéry numbers, Approximations of tangent polynomials, tangent-Bernoulli and tangent-Genocchi polynomials in terms of hyperbolic functions, Quantum Jacobi forms and sums of tails identities, Maass forms and the mock theta function \(f(q)\), Uniform bounds for sums of Kloosterman sums of half integral weight, Kac-Wakimoto characters and non-holomorphic Jacobi forms, Generalization of the von Staudt-Clausen theorem, On the quantum density of states and partitioning an integer, Taylor coefficients of non-holomorphic Jacobi forms and applications, Universal mock theta functions as quantum Jacobi forms, Quantum Jacobi forms in number theory, topology, and mathematical physics, The space of local operators in perturbed conformal field theories, Polynomials generalizing binomial coefficients and their application to the study of Fermat's last theorem, On integrality of certain algebraic numbers associated with modular forms, Reflection groups of Lorentzian lattices, Higher mathematics with the beam scale, A simple evaluation of a theta value, the Kronecker limit formula and a formula of Ramanujan, Tauberian and Mercerian theorems for systems of kernels, Paper folding, theta functions and the circle method, Jagged partitions, \(q\)-fractional Askey-Wilson integrals and related semigroups of operators, Certain modular functions similar to the Dedekind eta function., De Moivre and Bell polynomials, On multiplier systems and theta functions of half-integral weight for the Hilbert modular group \(\operatorname{SL}_2(\mathfrak{o})\), Equidistribution of Hecke eigenforms on the arithmetic surface \(\Gamma_0(N)\setminus {\mathbb H}\)., On Jacobi forms, and explicit evaluations of some trigonometric sums, On the vanishing of coefficients of the powers of a theta function, Elliptic functions and temperature inversion symmetry on spheres, Maass-Jacobi Poincaré series and Mathieu moonshine, Derivatives of Dedekind sums and their reciprocity law., On the size of the Durfee square of a random integer partition