$${\mathbb {Q}}$$ Q -linear dependence of certain Bessel moments

The Ramanujan Journal - Let $$I_0$$ and $$K_0$$ be modified Bessel functions of the zeroth order. We use Vanhove’s differential operators for Feynman integrals to derive upper bounds for...     

$$\Gamma $$ Γ -evaluations of hypergeometric series

The Ramanujan Journal - In this paper we explore special values of Gaussian hypergeometric functions in terms of products of Euler $$\Gamma $$ -functions and exponential functions of linear...     

Klingen $${\mathfrak {p}}^2$$ p 2 vectors for $$\mathrm{GSp}(4)$$ GSp ( 4 )

The Ramanujan Journal - We calculate the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $${\mathfrak {p}}^2$$ for all irreducible, admissible...     

Ramanujan-type $$1/\pi $$ -series from bimodular forms

The Ramanujan Journal - We develop an approach to establish $$1/\pi $$ -series from bimodular forms. Utilizing this approach, we obtain new families of 2-variable $$1/\pi $$ -series associated to...     

Divisibility of certain $$\ell $$ -regular partitions by 2

The Ramanujan Journal - For a positive integer $$\ell $$ , let $$b_{\ell }(n)$$ denote the number of $$\ell $$ -regular partitions of a nonnegative integer n. Motivated by some recent conjectures...     

Infinite series identities derived from the very well-poised $$\Omega $$ Ω -sum

The Ramanujan Journal - For the very well-poised $$\Omega $$ -series, a universal iteration pattern is established that yields numerous infinite series identities including several important ones...     

A method for proving Ramanujan’s series for $$1/\pi $$1/π

The Ramanujan Journal - For every group of order at most 14 we determine the values taken by its group determinant when its variables are integers.     

Some remarks on Kida’s formula when $$\mu \ne 0$$ μ ≠ 0

The Ramanujan Journal - Kida’s formula in classical Iwasawa theory relates the Iwasawa $$\lambda $$ -invariants of p-extensions of number fields. Analogue of this formula was subsequently...     

Algebraicity of critical values of adjoint L-functions for $$\mathrm{GSp}_4$$

The Ramanujan Journal - We prove an algebraicity result for certain critical value of adjoint L-functions for $$\mathrm{GSp}_4$$ over a totally real number field in terms of the Petersson norm of...     

Congruences for the coefficients of the mock theta function $$\beta (q)$$ β ( q )

The Ramanujan Journal - In this paper, we investigate the arithmetic properties for the coefficients of a sixth-order mock theta function $$\beta (q)$$ , which arose in the modular transformation...     

A note on shifted convolution of cusp-forms with $$\theta $$-series

Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function p(n). Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without the need for Hecke operators. In this paper, we give a method for generalizing Lachterman, Schayer, and Younger’s proof to include Ramanujan congruences for multipartition functions \(p_k(n)\) and Ramanujan congruences for p(n) modulo certain prime powers.     

On the distribution of the zeros of Eisenstein series for $$\Gamma _0^*(5)$$ Γ 0 ∗ ( 5 ) and $$\Gamma _0^*(7)$$ Γ 0 ∗ ( 7 )

The Ramanujan Journal - The goal of the present paper is to show that all the zeros of the Eisenstein series for $$\Gamma _0^*(5)$$ and $$\Gamma _0^*(7)$$ on the standard fundamental domain lie on...     

On two supercongruences of truncated hypergeometric series $${}_{4}F_{3}$$ 4 F 3

The Ramanujan Journal - In this paper, we prove two supercongruences conjectured by Sun via the Wilf–Zeilberger method. One of them is, for any prime $$p>3$$ , $$\begin{aligned}...     

Modularity of two double covers of $${\pmb {\mathbb {P}}}^5$$ P 5 branched along 12 hyperplanes

The Ramanujan Journal - For two varieties of dimension 5 constructed as double covers of $$\mathbb {P}^5$$ branched along the union of 12 hyperplanes, we prove that the number of points...     

Godement–Jacquet integrals on $$\mathrm{GL}(n,{\mathbf C})$$ GL ( n,C )

The Ramanujan Journal - We explicitly compute the complex archimedean part of the Godement–Jacquet zeta integral. We give a pair of a Schwartz–Bruhat function and a matrix coefficient...     

On the error term $$\Delta _{(k,l)}(x)$$ Δ ( k,l ) ( x )

The Ramanujan Journal - Let k, l be non-negative integers and $$\zeta ^{(k)}(s)$$ denote the kth derivative of the Riemann zeta function $$\zeta (s).$$ Further let $$d_{(k,l)}(n)$$ be the nth...     

Darboux evaluations for hypergeometric functions with the projective monodromy $$\hbox {PSL}(2,\mathbb {F}_7)$$ PSL ( 2 , F 7 )

The Ramanujan Journal - Algebraic hypergeometric functions can be compactly expressed as radical functions on pull-back curves where the monodromy group is simpler, say, a finite cyclic group....     

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in $$\mathbb {F}_{q}[T]$$ F q [ T ]

The Ramanujan Journal - In this paper, we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of...     

A family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$(p-1)/2 with both class numbers divisible by p

The Ramanujan Journal - Let p be a prime number with $$p\equiv 5\ (\mathrm{mod}\ {8})$$. We construct a new infinite family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$ with both class...     

The $${\mathbb {Q}}$$ Q -Korselt set of $$\mathrm {pq}$$ pq

Periodica Mathematica Hungarica - Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus...