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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
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...
On higher congruences between cusp forms and Eisenstein series
higher congruences cusp forms Eisenstein series Number Theory
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...
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
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
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
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...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
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
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
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.
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...
Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for P p−1 2 k=0 2k k 2 m−k (mod p2). In particular, we confirm se...
Congruences for Andrews' spt-function modulo powers of 5, 7 and 13
Andrews' spt-function math
2010/11/15
Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 a...
Power multiples in binary recurrence sequences: an approach by congruences
Power multiples binary recurrence sequences approach by congruences
2010/12/13
We introduce an elementary congruence-based procedure to look for q-th power multiples in arbitrary binary recurrence sequences (q 3). The procedure allows to prove that no such multiples exist in m...
A new series for $\pi^3$ and related congruences
Series for 3 central binomial coefficients congruences modulo prime powers
2010/12/14
Let H(2)n denote the second-order harmonic numberP0or n = 0, 1, 2, . . . . In this paper we obtain the following new identity for 3: 1 X k=1 2kH(2) k−1 k2k k = 3 48 .We e...