# Prym Differentials on Variable Tori

## Abstract

We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.

- Authors:

- Kemerovo State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771402

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DIFFERENTIAL CALCULUS; FUNCTIONS; MATHEMATICAL SPACE; RECIPROCAL V LAW; TORI; VECTORS

### Citation Formats

```
Krepitsina, T. S., E-mail: KC-Fabira@mail.ru, and Chueshev, V. V., E-mail: vvchueshev@mail.ru.
```*Prym Differentials on Variable Tori*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3729-9.

```
Krepitsina, T. S., E-mail: KC-Fabira@mail.ru, & Chueshev, V. V., E-mail: vvchueshev@mail.ru.
```*Prym Differentials on Variable Tori*. United States. doi:10.1007/S10958-018-3729-9.

```
Krepitsina, T. S., E-mail: KC-Fabira@mail.ru, and Chueshev, V. V., E-mail: vvchueshev@mail.ru. Sun .
"Prym Differentials on Variable Tori". United States. doi:10.1007/S10958-018-3729-9.
```

```
@article{osti_22771402,
```

title = {Prym Differentials on Variable Tori},

author = {Krepitsina, T. S., E-mail: KC-Fabira@mail.ru and Chueshev, V. V., E-mail: vvchueshev@mail.ru},

abstractNote = {We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.},

doi = {10.1007/S10958-018-3729-9},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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