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Displaying 481 – 500 of 906

Congruences for ${(A + \sqrt (A ² + m B ²))}^{(p - 1) / 2)}$ and ${(b + \sqrt (a ² + b ²))}^{(p - 1) / 4} (m o d p)$

Zhi-Hong Sun (2011)

Acta Arithmetica

Congruences for a class of alternating lacunary sums of binomial coefficients.

Dilcher, Karl (2007)

Journal of Integer Sequences [electronic only]

Congruences for certain binomial sums

Jung-Jo Lee (2013)

Czechoslovak Mathematical Journal

We exploit the properties of Legendre polynomials defined by the contour integral $𝐏_{n} (z) = {(2 π i)}^{- 1} \oint {(1 - 2 t z + t^{2})}^{- 1 / 2} t^{- n - 1} d t,$ where the contour encloses the origin and is traversed in the counterclockwise direction, to obtain congruences of certain sums of central binomial coefficients. More explicitly, by comparing various expressions of the values of Legendre polynomials, it can be proved that for any positive integer $r$ , a prime $p ⩾ 5$ and $n = r p^{2} - 1$ , we have $\sum_{k = 0}^{⌊ n / 2 ⌋} (\binom{2 k}{k}) \equiv 0, 1 or - 1 (mod p^{2})$ , depending on the value of $r (mod 6)$ .

Congruences for certain families of Apéry-like sequences

Zhi-Hong Sun (2022)

Czechoslovak Mathematical Journal

We systematically investigate the expressions and congruences for both a one-parameter family ${G_{n} (x)}$ as well as a two-parameter family ${G_{n} (r, m)}$ of sequences.

Congruences for Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two.

Shin-ichiro Mizumoto (1986)

Mathematische Annalen

Congruences for Eigenvalues of Hecke Operators on SL2(Z).

Kazuyuki Hatada (1981)

Manuscripta mathematica

Congruences for hyper $m$ -ary overpartition functions.

Ma, Lin, Lu, Qing-Lin (2010)

Integers

Congruences for m-ary partitions.

Gunnar Dirdal (1975)

Mathematica Scandinavica

Congruences for $q^{[p / 8]} (m o d p)$

Zhi-Hong Sun (2013)

Acta Arithmetica

Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of the integers m and n. Let p ≡ 1 (mod 4) be a prime, q ∈ ℤ, 2 ∤ q and p=c²+d²=x²+qy² with c,d,x,y ∈ ℤ and c ≡ 1 (mod 4). Suppose that (c,x+d)=1 or (d,x+c) is a power of 2. In this paper, by using the quartic reciprocity law, we determine $q^{[p / 8]} (m o d p)$ in terms of c,d,x and y, where [·] is the greatest integer function. Hence we partially solve some conjectures posed in our previous two papers.

Congruences for Ramanujan's ϕ function

Song Heng Chan (2012)

Acta Arithmetica

Congruences for representations of primes by binary quadratic forms

Richard Hudson, Kenneth Williams (1982)

Acta Arithmetica

Congruences for Siegel modular forms

Dohoon Choi, YoungJu Choie, Olav K. Richter (2011)

Annales de l’institut Fourier

We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree $2$ . In particular, we determine when an analog of Atkin’s $U (p)$ -operator applied to a Siegel modular form of degree $2$ is nonzero modulo a prime $p$ . Furthermore, we discuss explicit examples to illustrate our results.

Currently displaying 481 – 500 of 906

Previous Page 25 Next

Displaying 481 – 500 of 906

Congruences for ${(A + \sqrt (A ² + m B ²))}^{(p - 1) / 2)}$ and ${(b + \sqrt (a ² + b ²))}^{(p - 1) / 4} (m o d p)$

Congruences for a class of alternating lacunary sums of binomial coefficients.

Congruences for certain binomial sums

Congruences for certain families of Apéry-like sequences

Congruences for Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two.

Congruences for Eigenvalues of Hecke Operators on SL2(Z).

Congruences for hyper $m$ -ary overpartition functions.

Congruences for m-ary partitions.

Congruences for $q^{[p / 8]} (m o d p)$

Congruences for Ramanujan's ϕ function

Congruences for representations of primes by binary quadratic forms

Congruences for Siegel modular forms

Congruences for Stirling numbers and Eulerian numbers

Congruences for the coefficients of quotients of Eisenstein series

Congruences for the Coefficients of the Modular Invariant j(...).

Congruences for the Coefficients of the Modular Invariant j(...).

Congruences for the Convolution of Divisor sum function

Congruences for the Fourier coefficients of certain modular forms.

Congruences for the partition function modulo powers of 5

Congruences for the Stirling numbers and associated Stirling numbers

Currently displaying 481 – 500 of 906