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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Identities, inequalities and congruences for odd ranks and k-marked odd Durfee symbols
奇数秩 k标记 奇数杜菲符号 恒等式 不等式 全等
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2023/4/23
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
Congruences of Multipartition Functions Modulo Powers of Primes
modular form partition multipartition Ramanujan-type congruence
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2014/6/3
Let pr(n) denote the number of r-component multipartitions of n, and let Sγ λ be the space spanned by η(24z)γφ(24z), where η(z) is the Dedekind’s eta function and η(z) is a holomorphic modular form i...
On higher congruences between cusp forms and Eisenstein series
higher congruences cusp forms Eisenstein series Number Theory
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2012/6/30
In this paper we present several finite families of congruences between cusp forms and Eisenstein series of higher weights at powers of prime ideals. We formulate a conjecture which describes properti...
Congruences for L-functions of additive exponential sums
Character sums L-functions
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2012/6/27
We give a congruence for L-functions coming from affine additive exponential sums over a finite field. Precisely, we give a congruence for certain operators coming from Dwork's theory. This congruence...
Quadratic congruences on average and rational points on cubic surfaces
Quadratic congruences rational points Manin’s conjecture cubic surfaces universal torsors
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2012/5/24
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
Heegner points and Jochnowitz congruences on Shimura curves
Heegner points Shimura curves L-functions Jochnowitz congruences
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2012/4/18
Given a rational elliptic curve E, a suitable imaginary quadratic field K and a quaternionic Hecke eigenform g of weight 2 obtained from E by level raising such that the sign in the functional equatio...
Ramanujan type congruences for modular forms of several variables
Congruences for modular forms Cusp forms Number Theory
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2012/4/17
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence o...
Decompositions of commutative monoid congruences and binomial ideals
Decompositions of commutative monoid congruences binomial ideals Commutative Algebra
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2011/9/19
Abstract: We demonstrate how primary decomposition of commutative monoid congruences fails to capture the essence of primary decomposition in commutative rings by exhibiting a more sensitive theory of...
Unique path partitions: Characterization and Congruences
binary partitions unique path partitions rim hooks symmetric group character values congruences
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2011/8/26
Abstract: We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.
Congruences for Bipartitions with Odd Parts Distinct
partition bipartition congruence birank
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2014/6/3
Hirschhorn and Sellers studied arithmetic properties of the number of partitions with odd parts distinct. In another direction, Hammond and Lewis investigated arithmetic properties of the number of bi...
Congruences for central binomial sums and finite polylogarithms
Congruences central binomial sums finite polylogarithms
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2011/1/19
(This is still a preliminary draft: the proofs are complete, but the exposition will be improved in the next version.) We prove congruences, modulo a power of a prime p, for certain finite sums involv...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
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2011/2/22
Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence {Un} given by U0 = 1 and Un = −2P[n/2] k=1 n 2kUn−2k (n 1), and establish many recursi...
Some Congruences of Kloosterman Sums and their Minimal Polynomials
Congruences of Kloosterman Sums Minimal Polynomials
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2011/1/18
We prove two results on Kloosterman sums over finite fields, using Stickelberger’s theorem and the Gross-Koblitz formula. The first result concerns the minimal polynomial over Q of a Kloosterman sum, ...
Congruences concerning Legendre polynomials II
Legendre polynomial congruence character sum binary quadratic form
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2011/2/22
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W.
Congruences concerning Legendre polynomials III
Congruences Legendre polynomials III
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2011/2/23
Let p > 3 be a prime, and let m be an integer with p ∤ m. In the paper we solve some conjectures of Z.W. Sun concerning Pp−1 k=0 (6k)! mk(3k)!k!3 (mod p), and show that for integers m, n w...