Modular properties of elliptic Bernoulli and Euler functions
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Bernoulli and Euler numbers play an important and quite mysterious role in mathematics and in various places like analysis, number theory, di erential geometry and algebraic topology. In the rst part of this paper, we present old, recent and new results of Bernoulli(resp. Euler) numbers, polynomials and functions. We also discuss the relationship which exists between Bernoulli and Euler objects. In the second part of this paper we introduce their elliptic analogues. This part is completely new. Our method and results are quite similar to the classical one except the use of elliptic functions and Jacobi forms. We introduce elliptic Bernoulli and Euler numbers and functions and we study their properties. In fact we show the Raabe formulae satis ed by these functions. Our new results are the theorems 1.4.2, 2.3.1, 2.4.1, 2.4.2.
Abstract
Bernoulli and Euler numbers play an important and quite mysterious role in mathematics and in various places like analysis, number theory, di erential geometry and algebraic topology. In the rst part of this paper, we present old, recent and new results of Bernoulli(resp. Euler) numbers, polynomials and functions. We also discuss the relationship which exists between Bernoulli and Euler objects. In the second part of this paper we introduce their elliptic analogues. This part is completely new. Our method and results are quite similar to the classical one except the use of elliptic functions and Jacobi forms. We introduce elliptic Bernoulli and Euler numbers and functions and we study their properties. In fact we show the Raabe formulae satis ed by these functions. Our new results are the theorems 1.4.2, 2.3.1, 2.4.1, 2.4.2.
참고문헌 (28)
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