Euler sums with Dirichlet characters
Euler system for Galois deformations
In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation and the...
Euler systems obtained from congruences between Hilbert modular forms
Eulerian numbers and operators.
Eulerian numbers, Foulkes characters and Lefschetz characters of the symmetric group.
Eulerian numbers with fractional order parameters.
Eulerprodukte und diskrete Mittelwerte.
Euler's concordant forms
Euler's function and the sum of divisors.
Euler’s Partition Theorem
In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].
Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence
In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.
Évaluation asymptotique de l'ordre maximum d'un élément du groupe symétrique
Évaluation d'une somme arithmétique associée à une forme modulaire non analytique
Évaluation d'une somme arithmétique. Remarques
Evaluation effective du nombre d'entiers n tels que φ(n) ≤ x
Evaluation of divisor functions of matrices
1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped us obtain...
Evaluation of Euler-Zagier sums.
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Evaluation of the sums
The convolution sum is evaluated for and all . This completes the partial evaluation given in the paper of J. G. Huard, Z. M. Ou, B. K. Spearman, K. S. Williams.
Evaluation of triple Euler sums.