EuDML | Browse

Let $f = \sum_{n = 1}^{\infty} a (n) q^{n}$ and $g = \sum_{n = 1}^{\infty} b (n) q^{n}$ be holomorphic common eigenforms of all Hecke operators for the congruence subgroup $Γ_{0} (N)$ of $S L_{2} (Z)$ with “Nebentypus” character $ψ$ and $ξ$ and of weight $k$ and $ℓ$ , respectively. Define the Rankin product of $f$ and $g$ by $𝒟_{N} (s, f, g) = (\sum_{n = 1}^{\infty} ψ ξ (n) n^{k + ℓ - 2 s - 2}) (\sum_{n = 1}^{\infty} a (n) b (n) n^{- s}) .$ Supposing $f$ and $g$ to be ordinary at a prime $p \geq 5$ , we shall construct a $p$ -adically analytic $L$ -function of three variables which interpolate the values $\frac{𝒟_{N} (ℓ + m, f, g)}{π^{ℓ + 2 m + 1} < f, f >}$ for integers $m$ with $0 \leq m < k - 1,$ by regarding all the ingredients $m$ , $f$ and $g$ as variables. Here $⟨ f, f ⟩$ is the Petersson self-inner product of $f$ .

A $p$ -adic regulator map and finiteness results for arithmetic schemes.

Saito, S., Sato, K. (2010)

Documenta Mathematica

A $p$ -adic study of the partial sums of the harmonic series.

Boyd, David W. (1994)

Experimental Mathematics

A p-adic integral representation of the p-adic L-function.

Yasuo Morita (1978)

Journal für die reine und angewandte Mathematik

A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I.

Haruzo Hida (1985)

Inventiones mathematicae

A p-adic Nevanlinna-Diophantine correspondence

Ta Thi Hoai An, Aaron Levin, Julie Tzu-Yueh Wang (2011)

Acta Arithmetica

A p-adic Perron-Frobenius theorem

Robert Costa, Patrick Dynes, Clayton Petsche (2016)

Acta Arithmetica

We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.

A paintability version of the combinatorial Nullstellensatz, and list colorings of $k$ -partite $k$ -uniform hypergraphs.

Schauz, Uwe (2010)

The Electronic Journal of Combinatorics [electronic only]

Currently displaying 701 – 720 of 1964

Previous Page 36 Next

Displaying 701 – 720 of 1964

A note to the transcendence of special infinite series

A notion of density and essential components in GF[p,x]

A notion of diaphony based on p-adic arithmetic

A number-theoretic conjecture and its implication for set theory.

A numerical bound for small prime solutions of some ternary linear equations

A numerical sampling problem and the Weyl pseudorandom numbers.

A $p$ -adic measure attached to the zeta functions associated with two elliptic modular forms. II

A $p$ -adic regulator map and finiteness results for arithmetic schemes.

A $p$ -adic study of the partial sums of the harmonic series.

A p-adic integral representation of the p-adic L-function.

A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I.

A p-adic Nevanlinna-Diophantine correspondence

A p-adic Perron-Frobenius theorem

A paintability version of the combinatorial Nullstellensatz, and list colorings of $k$ -partite $k$ -uniform hypergraphs.

A parametric family of elliptic curves

A parametric family of quartic Thue equations

A parametric family of sextic Thue equations

A parametrization of equilateral triangles having integer coordinates.

A partition formula for Fibonacci numbers.

A partition identity with certain applications

Currently displaying 701 – 720 of 1964