Found 587 Documents (Results 1–100)
Approximation and inequalities for the factorial function related to the Burnside’s formula. (English) Zbl 07910622
Trigonometric analogues of the identities associated with twisted sums of divisor functions. (English) Zbl 07887388
Reviewer: Sami Omar (Sukhair)
A Dirichlet character analogue of Ramanujan’s formula for odd zeta values. (English) Zbl 07873206
Reviewer: Shigeru Kanemitsu (Kitakyūshū)
A note on odd zeta values over any number field and extended Eisenstein series. (English) Zbl 07852395
Reviewer: Sami Omar (Sukhair)
Congruences modulo powers of 5 for Ramanujan’s \(\phi\) function. (English) Zbl 07837271
Reviewer: Manjil Pratim Saikia (Ahmedabad)
Infinite families of solutions for \(A^3 + B^3 = C^3 + D^3\) and \(A^4 + B^4 + C^4 + D^4 + E^4 = F^4\). (English) Zbl 1541.11031
Reviewer: Yong Zhang (Changsha)
MSC:
11D25
On Ramanujan’s lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions. (English) Zbl 07815315
Extended higher Herglotz functions. I: Functional equations. (English) Zbl 07796442
Reviewer: Masanari Kida (Tōkyō)
On the Epstein zeta function and the zeros of a class of Dirichlet series. (English) Zbl 07758995
Reviewer: Sami Omar (Sukhair)
On the identities of Ramanujan – a \(q\)-series approach. (English) Zbl 1540.33018
Reviewer: Rózsa Horváth-Bokor (Budakalász)
Ancient Indian mathematics needs an honorific place in modern mathematics celebration. (English) Zbl 1530.01006
MSC:
01A32
Radius of \(\gamma\)-spirallikeness of order \(\alpha\) of some special functions. (English) Zbl 1530.30019
Modular identities and dissections of continued fractions of order thirty-two. (English) Zbl 1534.11005
Reviewer: Takao Komatsu (Hangzhou)
Generalizations of mock theta functions and Appell-Lerch sums. (English) Zbl 1539.33013
Reviewer: Navneet Lal Sharma (Vadodara)
Two general series identities involving modified Bessel functions and a class of arithmetical functions. (English) Zbl 1537.33004
Reviewer: Joshua Zelinsky (New Haven)
Exact evaluations and reciprocity theorems for finite trigonometric sums. (English) Zbl 1534.11101
Reviewer: Mehdi Hassani (Zanjan)
Explicit transformations for generalized Lambert series associated with the divisor function \(\sigma_a^{(N)}(n)\) and their applications. (English) Zbl 1540.11111
Reviewer: Shigeru Kanemitsu (Kitakyūshū)
On Rogers-Ramanujan-Slater type theta function identity. (English) Zbl 1539.11136
Reviewer: Ljuben Mutafchiev (Sofia)
Ramanujan’s formula for odd zeta values: a proof by Mittag-Leffler expansion and applications. (English) Zbl 07740685
Reviewer: Sami Omar (Sukhair)
Analogue of Ramanujan’s function \(k (\tau)\) for the cubic continued fraction. (English) Zbl 07739858
Reviewer: Noburo Ishii (Kyōto)
New proofs of some double sum Rogers-Ramanujan type identities. (English) Zbl 07739356
Reviewer: Yong-Gao Chen (Nanjing)
Congruences for the coefficients of a pair of third and sixth order mock theta functions. (English) Zbl 1532.11143
Reviewer: Maxie D. Schmidt (Atlanta)
Families of identities involving universal mock theta functions. (English) Zbl 1533.33025
Reviewer: M. P. Chaudhary (New Delhi)
A polynomial method for proving congruences of \(p_\omega(n,m)\) and \(p_\nu(n,m)\). (English) Zbl 1527.11080
Reviewer: Mircea Merca (Cornu de Jos)
A new approach to the Dyson rank conjectures. (English) Zbl 1525.11120
Reviewer: Dazhao Tang (Chongqing)
The Kronecker theta function and a decomposition theorem for theta functions. I. (English) Zbl 1529.11067
Reviewer: Dazhao Tang (Chongqing)
Identities associated to a generalized divisor function and modified Bessel function. (English) Zbl 1521.11054
Reviewer: Stelian Mihalas (Timişoara)
Two generalizations of Jacobi’s triple product identity and their applications. (English) Zbl 1519.11020
Reviewer: İlker İnam (Bilecik)
Differential transcendence of solutions for \(q\)-difference equation of Ramanujan function. (English) Zbl 1515.39003
Filipuk, Galina (ed.) et al., Recent trends in formal and analytic solutions of diff. equations. Virtual conference, University of Alcalá, Alcalá de Henares, Spain, June 28 – July 2, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 782, 143-153 (2023).
Reviewer: Alexander B. Levin (Washington)
On string functions and double-sum formulas. (English) Zbl 1539.11070
Reviewer: Matthew Krauel (Sacramento)
Rogers-Ramanujan type identities and Chebyshev polynomials of the third kind. (English) Zbl 1511.05016
A new Ramanujan-type identity for \(L(2k+1, \chi_1)\). (English) Zbl 1517.11104
Reviewer: Stelian Mihalas (Timişoara)
A conjecture of Baruah and Begum on the smallest parts function of restricted overpartitions. (English) Zbl 1523.11186
Reviewer: Donna Q. J. Dou (Changchun)
New equalities and inequalities for the ranks and cranks of partitions. (English) Zbl 1515.11098
Reviewer: Mircea Merca (Cornu de Jos)
Extensions of Watson’s theorem and the Ramanujan-Guinand formula. (English) Zbl 1514.11053
Reviewer: Stelian Mihalas (Timişoara)
Proofs of conjectures of Chan for \(d(n)\). (English) Zbl 1512.11074
Reviewer: M. P. Chaudhary (New Delhi)
MSC:
11P83
A finite analogue of a \(q\)-series identity of Bhoria, Eyyunni and Maji and its applications. (English) Zbl 1509.11095
Reviewer: M. P. Chaudhary (New Delhi)
On explicit evaluation of ratio’s of theta function which is analogous to Ramanujan’s function \(a_{m,n}\). (English) Zbl 1539.11040
Theorems on analogous of Ramanujan’s remarkable product of theta-function and their explicit evaluations. (English) Zbl 07801799
Relations between mock theta functions and combinatorial partition identities. (English) Zbl 1531.11100
Reviewer: Ljuben Mutafchiev (Sofia)
Jacobi’s triple-product identity and an associated family of theta-function identities. (English) Zbl 1505.05023
Evaluation of convolution sums \(\sum_{l+15m=n} \sigma (l) \sigma (m)\) and \(\sum_{3l+5m=n} \sigma (l) \sigma (m)\). (English) Zbl 1501.11014
On incomplete elliptic integrals related to Ramanujan’s theta functions. (English) Zbl 1507.11035
Reviewer: C. L. Parihar (Indore)
Some new congruences for \((j, k)\)-regular bipartition triples. (English) Zbl 1509.11096
Reviewer: Donna Q. J. Dou (Changchun)
Product formula and allied properties for the bivariate partial theta function. (Chinese. English summary) Zbl 1513.33058
MSC:
33E30
A family of theta-function identities involving \(R_\alpha\) and \(R_m\)-functions related to Jacobi’s triple-product identity. (English) Zbl 1495.11056
Euler product asymptotics for Dirichlet \(L\)-functions. (English) Zbl 1501.11086
Reviewer: David Lowry-Duda (Providence)
Identities and inequalities for the \(M_2\)-rank of partitions without repeated odd parts modulo 8. (English) Zbl 1501.11095
Reviewer: Mihály Szalay (Budapest)
The sum of divisors function and the Riemann hypothesis. (English) Zbl 1497.11243
Reviewer: Mehdi Hassani (Zanjan)
Hecke-type triple sums associated with mock theta functions. (English) Zbl 1502.33008
Reviewer: Neha Malik (New Delhi)
Explicit transformations of certain Lambert series. (English) Zbl 1492.33006
Reviewer: Thomas Ernst (Uppsala)
Generalization of five \(q\)-series identities of Ramanujan and unexplored weighted partition identities. (English) Zbl 1489.11158
Generalizations of Dyson’s rank on overpartitions. (English) Zbl 1494.11081
Reviewer: Mircea Merca (Cornu de Jos)
Generalizations of the Andrews-Yee identities associated with the mock theta functions \(\omega (q)\) and \(\nu (q)\). (English) Zbl 1492.11143
Reviewer: Mircea Merca (Cornu de Jos)
Evaluation of convolution sums \(\sum\limits_{l + km = n} \sigma(l)\sigma(m)\) and \(\sum\limits_{al + bm = n} \sigma (l)\sigma (m)\) for \(k = a \cdot b = 21, 33\), and \(35\). (English) Zbl 1497.11017
Integral and series representations of \(q\)-polynomials and functions. III: Theta, Ramanujan and \(q\)-Bessel functions. (English) Zbl 1506.33010
A proof of the mod 4 unimodal sequence conjectures and related mock theta functions. (English) Zbl 1491.11042
Reviewer: M. P. Chaudhary (New Delhi)
Congruence properties of coefficients of the eighth-order mock theta function \(V_0(q)\). (English) Zbl 1498.11209
Reviewer: William J. Keith (Houghton)
Identities, inequalities and congruences for odd ranks and \(k\)-marked odd Durfee symbols. (English) Zbl 1491.11097
Reviewer: Rózsa Horváth-Bokor (Budakalász)
Balanced derivatives, identities, and bounds for trigonometric and Bessel series. (English) Zbl 1503.11109
Reviewer: Giovanni Coppola (Napoli)
Quantum Jacobi forms and sums of tails identities. (English) Zbl 1491.11051
Reviewer: Larry Rolen (Dublin)
A posteriori error estimates of spectral approximations for second order partial differential equations in spherical geometries. (English) Zbl 1490.65249
Some identities for the partition function. (English) Zbl 1503.11136
Reviewer: Mihály Szalay (Budapest)
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