Results 1 to 10 of about 349 (51)
Counting certain quadratic partitions of zero modulo a prime number
Open Mathematics, 2021 Consider an odd prime number p≡2(mod3)p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3). In this paper, the number of certain type of partitions of zero in Z/pZ{\mathbb{Z}}\hspace{-0.1em}\text{/}\hspace{-0.1em}p{\mathbb{Z}} is calculated using a ...
Xiao Wang, Li Aihua
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The false theta functions of Rodgers and their modularity
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 963-980, August 2021., 2021 Abstract In this survey article, we explain how false theta functions can be embedded into a modular framework and show some of the applications of this modularity.
Kathrin Bringmann
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Ramanujan-type congruences modulo 4 for partitions into distinct parts
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form Q(p⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left(
Merca Mircea
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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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Some congruences for 3-component multipartitions
Open Mathematics, 2016 Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34).
Zhao Tao Yan, Jin Lily J., Gu C.
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Proof of a Limited Version of Mao's Partition Rank Inequality using a Theta Function Identity [PDF]
, 2016 Ramanujan's congruence $p(5k+4) \equiv 0 \pmod 5$ led Dyson \cite{dyson} to conjecture the existence of a measure "rank" such that $p(5k+4)$ partitions of $5k+4$ could be divided into sub-classes with equal cardinality to give a direct proof of Ramanujan'
Barman, Rupam +1 more
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On the distribution of sums of residues [PDF]
, 1993 We generalize and solve the $\roman{mod}\,q$ analogue of a problem of Littlewood and Offord, raised by Vaughan and Wooley, concerning the distribution of the $2^n$ sums of the form $\sum_{i=1}^n\varepsilon_ia_i$, where each $\varepsilon_i$ is $0$ or $1$.
Griggs, Jerrold R.
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Parity results for broken 11-diamond partitions
Open Mathematics, 2019 Recently, Dai proved new infinite families of congruences modulo 2 for broken 11-diamond partition functions by using Hecke operators. In this note, we establish new parity results for broken 11-diamond partition functions.
Wu Yunjian
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On the counting function of sets with even partition functions [PDF]
, 2011 Let q be an odd positive integer and P \in F2[z] be of order q and such that P(0) = 1. We denote by A = A(P) the unique set of positive integers satisfying \sum_{n=0}^\infty p(A, n) z^n \equiv P(z) (mod 2), where p(A,n) is the number of partitions of n ...
Nicolas, Jean-Louis, Said, Fethi Ben
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On the existence of a non‐zero lower bound for the number of Goldbach partitions of an even integer
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 15, Page 789-798, 2004., 2004 The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non‐zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4.
Simon Davis
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