Zobrazeno 1 - 10
of 21
pro vyhledávání: '"David Penniston"'
Autor:
DAVID PENNISTON
Publikováno v:
Bulletin of the Australian Mathematical Society. :1-10
A partition of a positive integer n is called $\ell $ -regular if none of its parts is divisible by $\ell $ . Denote by $b_{\ell }(n)$ the number of $\ell $ -regular partitions of n. We give a complete characterisation of the arithmetic of $b_{23}(n)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba2beb36148a033d415de28bd154d4a9
https://doi.org/10.1017/s0004972722001393
https://doi.org/10.1017/s0004972722001393
Autor:
David Penniston
Publikováno v:
International Journal of Number Theory. 15:1251-1259
A partition of a positive integer [Formula: see text] is called [Formula: see text]-regular if none of its parts is divisible by [Formula: see text]. Let [Formula: see text] denote the number of 11-regular partitions of [Formula: see text]. In this p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::af4db1aaff1561c509d9bc6ab5f3372d
https://doi.org/10.1142/s1793042119500696
https://doi.org/10.1142/s1793042119500696
Autor:
David Penniston, Eric Boll
Publikováno v:
Bulletin of the Australian Mathematical Society. 93:410-419
Let $b_{\ell }(n)$ denote the number of $\ell$-regular partitions of $n$. In this paper we establish a formula for $b_{13}(3n+1)$ modulo $3$ and use this to find exact criteria for the $3$-divisibility of $b_{13}(3n+1)$ and $b_{13}(3n)$. We also give
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c5ca91738036f2c06530ad3d034c5694
https://doi.org/10.1017/s0004972715001434
https://doi.org/10.1017/s0004972715001434
Autor:
David Furcy, David Penniston
Publikováno v:
The Ramanujan Journal. 27:101-108
Let bl(n) denote the number of l-regular partitions of n. Recently Andrews, Hirschhorn, and Sellers proved that b4(n) satisfies two infinite families of congruences modulo 3, and Webb established an analogous result for b13(n). In this paper we prove
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::63d18bf18ca9ce0c20523f30d9399afb
https://doi.org/10.1007/s11139-011-9312-3
https://doi.org/10.1007/s11139-011-9312-3
Publikováno v:
Acta Arithmetica. 149:215-244
Let E be an elliptic curve defined over an abelian number field K of degree m. For a prime ideal p of OK of good reduction we consider E over the finite field OK/p and let ap(E) be the trace of the Frobenius morphism. If E does not have complex multi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b10813ec05a085007f818ba25cd56610
https://doi.org/10.4064/aa149-3-2
https://doi.org/10.4064/aa149-3-2
Autor:
David Penniston, Kathrin Bringmann
Publikováno v:
Proceedings of the American Mathematical Society. 137:825-833
We prove the existence of an infinite family of non-harmonic weak Maass forms of varying weights and Laplace eigenvalues having algebraic coefficients, and show that the coefficients of these forms satisfy congruences of Ramanujan type.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f4088719eeb273a8cd705c452add9e6a
https://doi.org/10.1090/s0002-9939-08-09541-5
https://doi.org/10.1090/s0002-9939-08-09541-5
Autor:
David Penniston
Publikováno v:
International Journal of Number Theory. :295-302
Let bℓ(n) denote the number of ℓ-regular partitions of n, where ℓ is prime and 3 ≤ ℓ ≤ 23. In this paper we prove results on the distribution of bℓ(n) modulo m for any odd integer m > 1 with 3 ∤ m if ℓ ≠ 3.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ce594c8dcf19dba6afd886ac1f5edba
https://doi.org/10.1142/s1793042108001341
https://doi.org/10.1142/s1793042108001341
Publikováno v:
Mathematical Research Letters. 15:459-470
We investigate arithmetic properties of the Fourier coefficients of certain harmonic weak Maass forms of weight $1/2$ and $3/2$. Each of the forms in question is the sum of a holomorphic function and a period integral of a theta series. In particular
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7e1edfa1a08dd76ffdea9e768a07b8c5
https://doi.org/10.4310/mrl.2008.v15.n3.a6
https://doi.org/10.4310/mrl.2008.v15.n3.a6
Autor:
Brian Dandurand, David Penniston
Publikováno v:
The Ramanujan Journal. 19:63-70
We give exact criteria for the l-divisibility of the l-regular partition function b l (n) for l∈{5,7,11}. These criteria are found using the theory of complex multiplication. In each case the first criterion given corresponds to the Ramanujan congr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3f037a2837ac742e10eb433272e43a20
https://doi.org/10.1007/s11139-007-9042-8
https://doi.org/10.1007/s11139-007-9042-8
Autor:
David Penniston
Publikováno v:
Journal of Number Theory. 94:320-325
Let b l ( n ) denote the number of l-regular partitions of n , where l is a positive power of a prime p . We study in this paper the behavior of b l ( n ) modulo powers of p . In particular, we prove that for every positive integer j , b l ( n ) lies
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::851f45245fe303e3f0e6908d15fe5b2a
https://doi.org/10.1006/jnth.2001.2736
https://doi.org/10.1006/jnth.2001.2736